First-Input-First-Output (FIFO) buffers are extensively used in contemporary digital processors and System-on-Chips (SoC). There are synchronous FIFOs and asycnrhonous FIFOs. And different sized FIFOs should be implem...First-Input-First-Output (FIFO) buffers are extensively used in contemporary digital processors and System-on-Chips (SoC). There are synchronous FIFOs and asycnrhonous FIFOs. And different sized FIFOs should be implemented in different ways. FIFOs are used not only for the pipeline design within a processor, for the inter-processor communication networks, for example Network-on-Chips (NoCs), but also for the peripherals and the clock domain crossing at the whole SoC level. In this paper, we review the interface, the circuit implementation, and the various usages of FIFOs in various levels of the digital design. We can find that the usage of FIFOs could greatly facilitate the signal storage, signal decoupling, signal transfer, power domain separation and power domain crossing in digital systems. We hope that more attentions are paid to the usages of synchronous and asynchronous FIFOs and more sophististicated usages are discovered by the digital design communities.展开更多
This paper examines the impact of power transmission network topology change on locational marginal price(LMP) in real-time power markets. We consider the case where the false status of circuit breakers(CBs) that bypa...This paper examines the impact of power transmission network topology change on locational marginal price(LMP) in real-time power markets. We consider the case where the false status of circuit breakers(CBs) that bypass topology error processing can generate an incorrect power system network topology, subsequently distorting the results of the state estimation and economic dispatch.The main goal of this paper is to assess the economic impact of this misconfigured network topology on realtime LMP in an entire power system with network congestion. To this end, we start with our prior result, a simple and analytical congestion price equation, which can be applied to any single line congestion scenario. This equation can be extended to better understand the degree to which the LMP at any bus changes due to any line status error. Furthermore, it enables a rigorous analysis of the relationship between the change in LMP at any bus with respect to any line error and various physical/economical grid conditions such as the bidding prices for marginal generators and the locations of the congested/erroneous lines. Numerical examples on the impact analysis of this topology error are illustrated in IEEE 14-bus and 118-bus systems.展开更多
With the rapid development of deep learning methods, the data-driven approach has shown powerful advantages over the model-driven one. In this paper, we propose an end-to-end autoencoder communication system based on ...With the rapid development of deep learning methods, the data-driven approach has shown powerful advantages over the model-driven one. In this paper, we propose an end-to-end autoencoder communication system based on Deep Residual Shrinkage Networks (DRSNs), where neural networks (DNNs) are used to implement the coding, decoding, modulation and demodulation functions of the communication system. Our proposed autoencoder communication system can better reduce the signal noise by adding an “attention mechanism” and “soft thresholding” modules and has better performance at various signal-to-noise ratios (SNR). Also, we have shown through comparative experiments that the system can operate at moderate block lengths and support different throughputs. It has been shown to work efficiently in the AWGN channel. Simulation results show that our model has a higher Bit-Error-Rate (BER) gain and greatly improved decoding performance compared to conventional modulation and classical autoencoder systems at various signal-to-noise ratios.展开更多
Accurate traffic prediction is crucial for an intelligent traffic system (ITS). However, the excessive non-linearity and complexity of the spatial-temporal correlation in traffic flow severely limit the prediction acc...Accurate traffic prediction is crucial for an intelligent traffic system (ITS). However, the excessive non-linearity and complexity of the spatial-temporal correlation in traffic flow severely limit the prediction accuracy of most existing models, which simply stack temporal and spatial modules and fail to capture spatial-temporal features effectively. To improve the prediction accuracy, a multi-head attention spatial-temporal graph neural network (MSTNet) is proposed in this paper. First, the traffic data is decomposed into unique time spans that conform to positive rules, and valuable traffic node attributes are mined through an adaptive graph structure. Second, time and spatial features are captured using a multi-head attention spatial-temporal module. Finally, a multi-step prediction module is used to achieve future traffic condition prediction. Numerical experiments were conducted on an open-source dataset, and the results demonstrate that MSTNet performs well in spatial-temporal feature extraction and achieves more positive forecasting results than the baseline methods.展开更多
This paper provides a survey on modeling and theories of networked control systems(NCS). In the first part,modeling of the different types of imperfections that affect NCS is discussed. These imperfections are quantiz...This paper provides a survey on modeling and theories of networked control systems(NCS). In the first part,modeling of the different types of imperfections that affect NCS is discussed. These imperfections are quantization errors,packet dropouts, variable sampling/transmission intervals, variable transmission delays, and communication constraints. Then follows in the second part a presentation of several theories that have been applied for controlling networked systems. These theories include: input delay system approach, Markovian system approach, switched system approach, stochastic system approach,impulsive system approach, and predictive control approach. In the last part, some advanced issues in NCS including decentralized and distributed NCS, cloud control system, and co-design of NCS are reviewed.展开更多
This paper focuses on the problem of stability analysis and controller design for a class of delay systems based on networked control systems. By introducing some free matrix variables, some criteria for stability ana...This paper focuses on the problem of stability analysis and controller design for a class of delay systems based on networked control systems. By introducing some free matrix variables, some criteria for stability analysis and observer-based control law design can be obtained by the solving of linear matrix inequalities. A numerical example is also offered to prove the effectiveness of the proposed method.展开更多
Network-induced delay and jitter are key factors causing performance degradation and instability of NCSs (networked control systems). The relationships between the sampling periods of the control loops, network-induce...Network-induced delay and jitter are key factors causing performance degradation and instability of NCSs (networked control systems). The relationships between the sampling periods of the control loops, network-induced delay and jitter were studied aimed at token-type networks. A jitter-dependent optimal bandwidth scheduling algorithm for NCSs is proposed, which tries to achieve a tradeoff between bandwidth occupancy and system performance. Simulation tests proved the effectiveness of this optimal scheduling algorithm.展开更多
The H_∞ performance analysis and controller design for linear networked control systems(NCSs) are presented.The NCSs are considered a linear continuous system with time-varying interval input delay by assuming that t...The H_∞ performance analysis and controller design for linear networked control systems(NCSs) are presented.The NCSs are considered a linear continuous system with time-varying interval input delay by assuming that the sensor is time-driven and the logic Zero-order-holder(ZOH) and controller are event-driven.Based on this model,the delay interval is divided into two equal subintervals for H_∞ performance analysis.An improved H_∞ stabilization condition is obtained in linear matrix inequalities(LMIs) framework by adequately considering the information about the bounds of the input delay to construct novel Lyapunov–Krasovskii functionals(LKFs).For the purpose of reducing the conservatism of the proposed results,the bounds of the LKFs differential cross terms are properly estimated without introducing any slack matrix variables.Moreover,the H_∞ controller is reasonably designed to guarantee the robust asymptotic stability for the linear NCSs with an H_∞ performance level γ.Numerical simulation examples are included to validate the reduced conservatism and effectiveness of our proposed method.展开更多
System reliability can produce a strong influence on the performance of the heat exchanger network(HEN).In this paper,an optimization method with system reliability analysis for flexible HEN by genetic/simulated annea...System reliability can produce a strong influence on the performance of the heat exchanger network(HEN).In this paper,an optimization method with system reliability analysis for flexible HEN by genetic/simulated annealing algorithms(GA/SA) is presented.Initial flexible arrangements of HEN is received by pseudo-temperature enthalpy diagram.For determining system reliability of HEN,the connections of heat exchangers(HEXs) and independent subsystems in the HEN are analyzed by the connection sequence matrix(CSM),and the system reliability is measured by the independent subsystem including maximum number of HEXs in the HEN.As for the HEN that did not meet system reliability,HEN decoupling is applied and the independent subsystems in the HEN are changed by removing decoupling HEX,and thus the system reliability is elevated.After that,heat duty redistribution based on the relevant elements of the heat load loops and HEX areas are optimized in GA/SA.Then,the favorable network configuration,which matches both the most economical cost and system reliability criterion,is located.Moreover,particular features belonging to suitable decoupling HEX are extracted from calculations.Corresponding numerical example is presented to verify that the proposed strategy is effective to formulate optimal flexible HEN with system reliability measurement.展开更多
This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception (SMC). A sequence of variables obeying Bernoulli...This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception (SMC). A sequence of variables obeying Bernoulli distribution are employed to model the randomly occurring communication delays which could be different for different state variables. A discrete switching function that is different from those in the existing literature is first proposed. Then, expressed as the feasibility of a linear matrix inequality (LMI) with an equality constraint, sufficient conditions are derived in order to ensure the globally mean-square asymptotic stability of the system dynamics on the sliding surface. A discrete-time SMC controller is then synthesized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.展开更多
The insertion of the communication network in the feedback control loop makes the analysis and design of a network control system more complex, and induces some issues that degrade the control system's performance an...The insertion of the communication network in the feedback control loop makes the analysis and design of a network control system more complex, and induces some issues that degrade the control system's performance and even cause system instability. The main aspects are focused on the stability analysis of Network Control Systems (NCSs) with network-induced delays, data packet dropouts, and multiple-packet transmission. These issues must be considered in the design of an NCS. This work summarizes the main research results, and remarks on some related handling approaches and techniques. The main purpose of the survey is to present the new research state of NCSs and to point out some fields of future work.展开更多
As a promising technology to completely transform how we architect, deploy, operate and manage various networks, software-based Network Function Virtualization(NFV) enables hardware-independent, flexible, fast and eff...As a promising technology to completely transform how we architect, deploy, operate and manage various networks, software-based Network Function Virtualization(NFV) enables hardware-independent, flexible, fast and efficient network service provision. With the increasing popularity of NFV paradigm, the Internet has also transformed to be a hybrid environment where NFV-based network entities coexist with traditional network devices. To facilitate our understanding, design, evaluate and manage of such novel network environment, there is a great need for a new NFV-compatible network measurement system which is still in absent so far. To bridge this gap, a system, named Software Defined Network Measurement System(SDNMS), is presented in this paper. Firstly, the architecture of SDNMS is proposed. In this architecture, a formal method to describe the working mode of the network measurement is defined. This method can also be utilized to generate a network measurement middle box(NMMB) in a specific location of the NFV network according to the customized description file, and to flexibly deploy the network measurement function. Secondly, the technology of virtual network measurement function(VNMF) combined with LXC is studied to form NMMB function. Thirdly, a control method is presented to control the start, stop, and update NMMB to form a specific network measurement system function. Finally, a prototype of SDNMS with network monitoring function to monitor network performance anomalies and locate faults is introduced. Experimental results have shown that SDNMS architecture and related technologies are feasible and effective to deploy and control network measurement functions in NFV networks. We hope SDNMS could provide a new method for practitioners to conduct network management and research at the age of NFV.展开更多
This paper deals with the stochastic stability of networked control systems with the presence of network- induced delay and transmitted data dropout. Based on the Lyapunov approach, sufficient conditions for the mean-...This paper deals with the stochastic stability of networked control systems with the presence of network- induced delay and transmitted data dropout. Based on the Lyapunov approach, sufficient conditions for the mean-square stability of the networked control system are derived subject that the sequence of transmission interval is driven by an identically independently distributed sequence and by a finite state Markov chain, respectively. Stabilization controllers are constructed in terms of linear matrix inequalities correspondingly. An example is provided to illustrate our results.展开更多
This paper is concerned with the problem of robust stability analysis for networked control systems (NCSs). A new NCS model is proposed under consideration of both the network-induced delay and parameter uncertainti...This paper is concerned with the problem of robust stability analysis for networked control systems (NCSs). A new NCS model is proposed under consideration of both the network-induced delay and parameter uncertainties. The parameter uncertainties appearing in NCSs are norm-bounded, and possibly time-varying. The conventional method and the descriptor system method are used to obtain maximum allowable delay bound (MADB) guaranteeing robust stability and stability of the NCSs, respectively, where the stability criteria are formulated in terms of linear matrix inequalities (LMIs). And the MADB can be derived by solving the feasibility problem of the corresponding LMI. Some numerical examples are provided to illustrate the effectiveness of the proposed method.展开更多
文摘First-Input-First-Output (FIFO) buffers are extensively used in contemporary digital processors and System-on-Chips (SoC). There are synchronous FIFOs and asycnrhonous FIFOs. And different sized FIFOs should be implemented in different ways. FIFOs are used not only for the pipeline design within a processor, for the inter-processor communication networks, for example Network-on-Chips (NoCs), but also for the peripherals and the clock domain crossing at the whole SoC level. In this paper, we review the interface, the circuit implementation, and the various usages of FIFOs in various levels of the digital design. We can find that the usage of FIFOs could greatly facilitate the signal storage, signal decoupling, signal transfer, power domain separation and power domain crossing in digital systems. We hope that more attentions are paid to the usages of synchronous and asynchronous FIFOs and more sophististicated usages are discovered by the digital design communities.
基金supported in part by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIP)(No.2015R1C1A1A01051890)part by the National Science Foundation DGE-1303378
文摘This paper examines the impact of power transmission network topology change on locational marginal price(LMP) in real-time power markets. We consider the case where the false status of circuit breakers(CBs) that bypass topology error processing can generate an incorrect power system network topology, subsequently distorting the results of the state estimation and economic dispatch.The main goal of this paper is to assess the economic impact of this misconfigured network topology on realtime LMP in an entire power system with network congestion. To this end, we start with our prior result, a simple and analytical congestion price equation, which can be applied to any single line congestion scenario. This equation can be extended to better understand the degree to which the LMP at any bus changes due to any line status error. Furthermore, it enables a rigorous analysis of the relationship between the change in LMP at any bus with respect to any line error and various physical/economical grid conditions such as the bidding prices for marginal generators and the locations of the congested/erroneous lines. Numerical examples on the impact analysis of this topology error are illustrated in IEEE 14-bus and 118-bus systems.
文摘With the rapid development of deep learning methods, the data-driven approach has shown powerful advantages over the model-driven one. In this paper, we propose an end-to-end autoencoder communication system based on Deep Residual Shrinkage Networks (DRSNs), where neural networks (DNNs) are used to implement the coding, decoding, modulation and demodulation functions of the communication system. Our proposed autoencoder communication system can better reduce the signal noise by adding an “attention mechanism” and “soft thresholding” modules and has better performance at various signal-to-noise ratios (SNR). Also, we have shown through comparative experiments that the system can operate at moderate block lengths and support different throughputs. It has been shown to work efficiently in the AWGN channel. Simulation results show that our model has a higher Bit-Error-Rate (BER) gain and greatly improved decoding performance compared to conventional modulation and classical autoencoder systems at various signal-to-noise ratios.
文摘Accurate traffic prediction is crucial for an intelligent traffic system (ITS). However, the excessive non-linearity and complexity of the spatial-temporal correlation in traffic flow severely limit the prediction accuracy of most existing models, which simply stack temporal and spatial modules and fail to capture spatial-temporal features effectively. To improve the prediction accuracy, a multi-head attention spatial-temporal graph neural network (MSTNet) is proposed in this paper. First, the traffic data is decomposed into unique time spans that conform to positive rules, and valuable traffic node attributes are mined through an adaptive graph structure. Second, time and spatial features are captured using a multi-head attention spatial-temporal module. Finally, a multi-step prediction module is used to achieve future traffic condition prediction. Numerical experiments were conducted on an open-source dataset, and the results demonstrate that MSTNet performs well in spatial-temporal feature extraction and achieves more positive forecasting results than the baseline methods.
基金Supported by National Natural Science Foundation of P. R. China (60325311, 60534010, 60572070, 60521003), the Program for Changjiang Scholars and Innovative Research Team in University (IRT0421)
文摘柔韧的 H 联网了控制方法因为有无常和时间的模糊系统推迟的 Takagi-Sugeno (T-S ) 被介绍。一个州的反馈控制器经由联网的控制系统(NCS ) 被设计理论。为有 H 性能的柔韧的稳定性的足够的状况被获得。在网络传播和包退学学生的导致网络的延期被分析。模拟结果显示出这个控制计划的有效性。
基金supported by the Deanship of Scientific Research(DSR) at KFUPM through Research Project(IN141048)
文摘This paper provides a survey on modeling and theories of networked control systems(NCS). In the first part,modeling of the different types of imperfections that affect NCS is discussed. These imperfections are quantization errors,packet dropouts, variable sampling/transmission intervals, variable transmission delays, and communication constraints. Then follows in the second part a presentation of several theories that have been applied for controlling networked systems. These theories include: input delay system approach, Markovian system approach, switched system approach, stochastic system approach,impulsive system approach, and predictive control approach. In the last part, some advanced issues in NCS including decentralized and distributed NCS, cloud control system, and co-design of NCS are reviewed.
基金Supported by National Naturai Science Foundation of China (61273104, 61021002, 61104097), and Projects of Major Interna-tional (Regional) Joint Research Program National Natural Science Foundation of China (61120106010)
基金This work was supported in part by the National High Technology Research and Development Program of China (863 Program) (2014A A06A503), the National Natural Science Foundation of China (61422 307, 61473269, 61673361, 61673350), the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars and Ministry of Education of China, the Youth Innovation Promotion Asso- ciation, Chinese Academy of Sciences, the Youth Top-notch Talent Support Program, the 1000-talent Youth Program, and the Youth Yangtze River Scholarship.
基金supported by the National Science Foundation of China (No.60474003)Hunan Provincial Natural Science Foundation of China (07JJ6126)the Postdoctoral Science Foundation of Central South University
文摘This paper focuses on the problem of stability analysis and controller design for a class of delay systems based on networked control systems. By introducing some free matrix variables, some criteria for stability analysis and observer-based control law design can be obtained by the solving of linear matrix inequalities. A numerical example is also offered to prove the effectiveness of the proposed method.
基金Project supported by the National Natural Science Foundation ofChina (Nos. 60074011 and 60174009), and Youth Science and Tech-nology Foundation of Shanxi Province (No. 20051020), China
文摘Network-induced delay and jitter are key factors causing performance degradation and instability of NCSs (networked control systems). The relationships between the sampling periods of the control loops, network-induced delay and jitter were studied aimed at token-type networks. A jitter-dependent optimal bandwidth scheduling algorithm for NCSs is proposed, which tries to achieve a tradeoff between bandwidth occupancy and system performance. Simulation tests proved the effectiveness of this optimal scheduling algorithm.
基金Project (61304046) supported by the National Natural Science Funds for Young Scholar of ChinaProject (F201242) supported by Natural Science Foundation of Heilongjiang Province,China
文摘The H_∞ performance analysis and controller design for linear networked control systems(NCSs) are presented.The NCSs are considered a linear continuous system with time-varying interval input delay by assuming that the sensor is time-driven and the logic Zero-order-holder(ZOH) and controller are event-driven.Based on this model,the delay interval is divided into two equal subintervals for H_∞ performance analysis.An improved H_∞ stabilization condition is obtained in linear matrix inequalities(LMIs) framework by adequately considering the information about the bounds of the input delay to construct novel Lyapunov–Krasovskii functionals(LKFs).For the purpose of reducing the conservatism of the proposed results,the bounds of the LKFs differential cross terms are properly estimated without introducing any slack matrix variables.Moreover,the H_∞ controller is reasonably designed to guarantee the robust asymptotic stability for the linear NCSs with an H_∞ performance level γ.Numerical simulation examples are included to validate the reduced conservatism and effectiveness of our proposed method.
文摘System reliability can produce a strong influence on the performance of the heat exchanger network(HEN).In this paper,an optimization method with system reliability analysis for flexible HEN by genetic/simulated annealing algorithms(GA/SA) is presented.Initial flexible arrangements of HEN is received by pseudo-temperature enthalpy diagram.For determining system reliability of HEN,the connections of heat exchangers(HEXs) and independent subsystems in the HEN are analyzed by the connection sequence matrix(CSM),and the system reliability is measured by the independent subsystem including maximum number of HEXs in the HEN.As for the HEN that did not meet system reliability,HEN decoupling is applied and the independent subsystems in the HEN are changed by removing decoupling HEX,and thus the system reliability is elevated.After that,heat duty redistribution based on the relevant elements of the heat load loops and HEX areas are optimized in GA/SA.Then,the favorable network configuration,which matches both the most economical cost and system reliability criterion,is located.Moreover,particular features belonging to suitable decoupling HEX are extracted from calculations.Corresponding numerical example is presented to verify that the proposed strategy is effective to formulate optimal flexible HEN with system reliability measurement.
基金supported by the Engineering and Physical Sciences Research Council(EPSRC)of the UK(No.GR/S27658/01)the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany
文摘This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception (SMC). A sequence of variables obeying Bernoulli distribution are employed to model the randomly occurring communication delays which could be different for different state variables. A discrete switching function that is different from those in the existing literature is first proposed. Then, expressed as the feasibility of a linear matrix inequality (LMI) with an equality constraint, sufficient conditions are derived in order to ensure the globally mean-square asymptotic stability of the system dynamics on the sliding surface. A discrete-time SMC controller is then synthesized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.
基金This work was supported by the Youth Natural Science Foundation of AUTS(No.2005YQ002)Natural Science Foundation of Anhui ProvincialEducation Department(No.2006KJ031B).
文摘The insertion of the communication network in the feedback control loop makes the analysis and design of a network control system more complex, and induces some issues that degrade the control system's performance and even cause system instability. The main aspects are focused on the stability analysis of Network Control Systems (NCSs) with network-induced delays, data packet dropouts, and multiple-packet transmission. These issues must be considered in the design of an NCS. This work summarizes the main research results, and remarks on some related handling approaches and techniques. The main purpose of the survey is to present the new research state of NCSs and to point out some fields of future work.
基金supported by National Natural Science Foundation of China (No. 61772271, 61379149)
文摘As a promising technology to completely transform how we architect, deploy, operate and manage various networks, software-based Network Function Virtualization(NFV) enables hardware-independent, flexible, fast and efficient network service provision. With the increasing popularity of NFV paradigm, the Internet has also transformed to be a hybrid environment where NFV-based network entities coexist with traditional network devices. To facilitate our understanding, design, evaluate and manage of such novel network environment, there is a great need for a new NFV-compatible network measurement system which is still in absent so far. To bridge this gap, a system, named Software Defined Network Measurement System(SDNMS), is presented in this paper. Firstly, the architecture of SDNMS is proposed. In this architecture, a formal method to describe the working mode of the network measurement is defined. This method can also be utilized to generate a network measurement middle box(NMMB) in a specific location of the NFV network according to the customized description file, and to flexibly deploy the network measurement function. Secondly, the technology of virtual network measurement function(VNMF) combined with LXC is studied to form NMMB function. Thirdly, a control method is presented to control the start, stop, and update NMMB to form a specific network measurement system function. Finally, a prototype of SDNMS with network monitoring function to monitor network performance anomalies and locate faults is introduced. Experimental results have shown that SDNMS architecture and related technologies are feasible and effective to deploy and control network measurement functions in NFV networks. We hope SDNMS could provide a new method for practitioners to conduct network management and research at the age of NFV.
基金National Natural Science Foundation of China (No.60874021, 60674046)Natural Science Foundation from JiangsuProvince (No.BK2007061)+1 种基金Natural Science Foundation from Jiangsu Provincial Department for Education (No.06KJB120088)Research Fundfor Doctoral Program of Nantong University (No.07B14).
文摘This paper deals with the stochastic stability of networked control systems with the presence of network- induced delay and transmitted data dropout. Based on the Lyapunov approach, sufficient conditions for the mean-square stability of the networked control system are derived subject that the sequence of transmission interval is driven by an identically independently distributed sequence and by a finite state Markov chain, respectively. Stabilization controllers are constructed in terms of linear matrix inequalities correspondingly. An example is provided to illustrate our results.
基金supported by the National Natural Science Foundation of China (No.60721062)863 Program of China (No.2006AA04Z182)+1 种基金Department of Science and Technology Project of Zhejiang Province (No.2006C31016)Science Foundation of Zhejiang SciTech University(No.0803817-Y)
文摘This paper is concerned with the problem of robust stability analysis for networked control systems (NCSs). A new NCS model is proposed under consideration of both the network-induced delay and parameter uncertainties. The parameter uncertainties appearing in NCSs are norm-bounded, and possibly time-varying. The conventional method and the descriptor system method are used to obtain maximum allowable delay bound (MADB) guaranteeing robust stability and stability of the NCSs, respectively, where the stability criteria are formulated in terms of linear matrix inequalities (LMIs). And the MADB can be derived by solving the feasibility problem of the corresponding LMI. Some numerical examples are provided to illustrate the effectiveness of the proposed method.