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Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems
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作者 曾庆山 曹广益 朱新坚 《Journal of Shanghai Jiaotong university(Science)》 EI 2004年第2期20-24,共5页
The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and n... The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems. 展开更多
关键词 fractional calculus fractional-order linear time-invariant systems CONTROLLABILITY OBSERVABILITY STABILITY
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The identification algorithm for commensurate order linear time-invariant fractional systems
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作者 王振滨 曹广益 朱新坚 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2005年第5期576-580,共5页
An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at... An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned. 展开更多
关键词 fractional systems COMMENSURATE linear time-invariant state-space representation system identification
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On Delay-independent Stability Criteria for Linear Time-delay Systems 被引量:4
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作者 Ai-Guo Wu Guang-Ren Duan 《International Journal of Automation and computing》 EI 2007年第1期95-100,共6页
Several LMI representations for delay-independence stability are proposed by applying Projection Lemma and the socalled "Small Scalar Method". These criteria realize the elimination of the products coupling the syst... Several LMI representations for delay-independence stability are proposed by applying Projection Lemma and the socalled "Small Scalar Method". These criteria realize the elimination of the products coupling the system matrices and Lyapunov matrices by introducing some additional matrices. When they are applied to robust stability analysis for polytopic uncertain systems, the vertex-dependent Lyapunov functions are allowed, so less conservative results can be obtained. A numerical example is employed to illustrate the effect of these proposed criteria. 展开更多
关键词 linear time-delay systems DELAY-INDEPENDENT Small Scalar Method conservativeness.
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Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs 被引量:4
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作者 Peng CUI Chenghui ZHANG 《控制理论与应用(英文版)》 EI 2008年第2期177-183,共7页
The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which... The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality(LMI). Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods. 展开更多
关键词 Singular time-delay systems Functional observer Reduced-order observer Output feedback stabilization linear matrix inequality(LMI)
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Design of H_∞ robust fault detection filter for nonlinear time-delay systems 被引量:4
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作者 BAI Lei-shi HE Li-ming +1 位作者 TIAN Zuo-hua SHI Song-jiao 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第10期1733-1741,共9页
In this paper, the robust fault detection filter (RFDF) design problems are studied for nonlinear time-delay systems with unknown inputs. First, a reference residual model is introduced to formulate the RFDF design pr... In this paper, the robust fault detection filter (RFDF) design problems are studied for nonlinear time-delay systems with unknown inputs. First, a reference residual model is introduced to formulate the RFDF design problem as an H∞ model-matching problem. Then appropriate input/output selection matrices are introduced to extend a performance index to the time-delay systems in time domain. The reference residual model designed according to the performance index is an optimal residual generator, which takes into account the robustness against disturbances and sensitivity to faults simultaneously. Applying robust H∞ optimization control technique, the existence conditions of the RFDF for nonlinear time-delay systems with unknown inputs are presented in terms of linear matrix inequality (LMI) formulation, independently of time delay. An illustrative design example is used to demonstrate the validity and applicability of the proposed approach. 展开更多
关键词 Nonlinear time-delay systems Robust fault detection filter iRFDF H∞ optimization linear matrix inequality (LMI)
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Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays 被引量:3
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作者 K. Ramakrishnan G. Ray 《International Journal of Automation and computing》 EI 2011年第4期490-492,共3页
In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality (LMI) variables is presented for a delay-dependent stability criterion reported recently in the Interna... In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality (LMI) variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective. 展开更多
关键词 Discrete-time systems additive time-delays delay-dependent stability stability criterion linear matrix inequality (LMI).
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Design of unknown input observer with H_∞ performance for linear time-delay systems 被引量:3
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作者 Fu Yanming Wu Di Zhang Peng Duan Guangren 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第3期606-610,共5页
A unknown input observer (UIO) design for a class of linear time-delay systems when the observer error can't completely decouple from unknown input is dealt with. A sufficient condition to its existence is presente... A unknown input observer (UIO) design for a class of linear time-delay systems when the observer error can't completely decouple from unknown input is dealt with. A sufficient condition to its existence is presented based on Lyapunov stability method. Design problem of the proposed observer is formulated in term of linear matrix inequalities. Two design problems of the observer with internal delay and without internal delay are formulated. Based on H∞ control theory in time-delay systems, the proposed observer is designed in term of linear matrix inequalities (LMI). A design algorithm is proposed. The effective of the proposed approach is illustrated by a numerical example. 展开更多
关键词 unknown input observer time-delay systems linear matrix inequalities.
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On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach 被引量:1
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作者 Weihai ZHANG Xuezhen LIU +1 位作者 Shulan KONG Qinghua LI 《控制理论与应用(英文版)》 EI 2006年第3期229-234,共6页
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix i... This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given. 展开更多
关键词 Nonlinear stochastic systems linear matrix inequality Asymptotic stability in probability time-delay systems
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Robust H_∞ controller design for a class of nonlinear fuzzy time-delay systems 被引量:1
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作者 Wang Miaoxin Liu Jizhen +1 位作者 Liu Xiangjie Liu Juncheng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第6期1286-1289,共4页
The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality(LMI) method, the problem of fuzzy r... The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality(LMI) method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level. 展开更多
关键词 fuzzy control robust H∞ control nonlinear uncertainty fuzzy time-delay systems linear matrixinequality.
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Delay-dependent guaranteed cost control for uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays
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作者 王常虹 姚秀明 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第3期357-362,共6页
In this paper,the problem of guaranteed cost control for a class of uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays and a given quadratic cost function are investigated. Attention... In this paper,the problem of guaranteed cost control for a class of uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays and a given quadratic cost function are investigated. Attention is focused on designing a memoryless state feedback control law such that the closed-loop system is robust stochastically stable and the closed-loop cost function value is not more than a specified upper bound,for all admissible uncertainties. The key features of the approach include the introduction of a new type of suitable stochastic Lyapunov functional and free weighting matrices techniques. Sufficient conditions for the existence of such controller are obtained in terms of a set of linear matrix inequalities. A numerical example is given to illustrate the less conservatism of the proposed techniques. 展开更多
关键词 guaranteed cost control Markovian jump linear systems time-delay linear matrix inqualities(LMIs).
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Simultaneous quadratic performance stabilization for linear time-delay systems
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作者 Chen Yuepeng Zhou Zude +1 位作者 Liu Huanbin Zhang Qingling 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第4期817-823,共7页
A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained... A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities (LMIs) which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method. 展开更多
关键词 linear matrix inequalities (LMIs) simultaneous stabilization discrete time-delay systems quadratic performance index.
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Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties 被引量:4
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作者 Liu Xiaohua Yang Yuanhua 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第3期590-597,共8页
The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is propo... The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain "min-max" optimization problems are converted into convex optimization problems solving by the linear matrix inequality (LMI), and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method. 展开更多
关键词 predictive control singular systems linear matrix inequality state observer time-delay UNCERTAINTY
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New delay-dependent robust stability and stabilization for uncertain T-S fuzzy time-delay systems under imperfect premise matching 被引量:4
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作者 张泽健 黄显林 +1 位作者 班晓军 高晓智 《Journal of Central South University》 SCIE EI CAS 2012年第12期3415-3423,共9页
To alleviate the conservativeness of the stability criterion for Takagi-Sugeno (T-S) fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function ... To alleviate the conservativeness of the stability criterion for Takagi-Sugeno (T-S) fuzzy time-delay systems, a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term, which was firstly u3ed to derive the stability criterion for T-S fuzzy time-delay systems. By the same approach, the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered. On the other hand, in order to enhance the design flexibility, a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed, which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model. By the numerical examples, the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains. For instance, when the allowable time-delay increases from 7.3 s to 12 s for an uncertain T-S fuzzy control system with time-delay, the norm of the feedback gains decreases from (34.299 2, 38.560 3) to (10.073 3, 11.349 0), respectively. Meanwhile, the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition of x(0) = [3 -1]. 展开更多
关键词 T-S fuzzy systems time-delay systems imperfect premise matching stability robust stability linear matrix inequality(LMI) STABILIZATION
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Exponential passive filtering for a class of nonlinear jump systems 被引量:3
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作者 He Shuping Liu Fei 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第4期829-837,共9页
The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlineariti... The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach. 展开更多
关键词 nonlinear Markov jump systems UNCERTAINTIES time-delayS passive filter exponentially stochastically stable linear matrix inequalities.
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Robust H-infinity filter design for uncertaintime-delay singular stochastic systems withMarkovian jump 被引量:3
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作者 Jianwei XIA 《控制理论与应用(英文版)》 EI 2007年第4期331-335,共5页
This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions ... This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method. 展开更多
关键词 linear matrix inequality Markovian jump Robust H-infinity filter Singular stochastic systems time-delay
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Integral sliding mode control of time-delay systems with mismatching uncertainties 被引量:3
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作者 Fu Zhao Yu Liu Xiuming Yao Baoku Su 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第2期273-280,共8页
A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system und... A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method. 展开更多
关键词 linear matrix inequality integral sliding mode control uncertain time-delay systems mismatching uncertainties.
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H_∞ Control Based on LMIs for a Class of Time-delay Switched Systems 被引量:2
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作者 李春明 田学民 《Journal of Measurement Science and Instrumentation》 CAS 2010年第3期293-296,共4页
The problem of H∞ stability analysis and control synthesis of switched systems with delayed states under arb/trary switchirg laws is considered. By means of Lyapunov function and linear matrix inequality tools, suffi... The problem of H∞ stability analysis and control synthesis of switched systems with delayed states under arb/trary switchirg laws is considered. By means of Lyapunov function and linear matrix inequality tools, sufficient ctmdition of H∞ stability is presented in terms of linear matrix inequalities. Furthermore, the robust H∞ control synthesis via state feedback and output feedack is studied. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. 展开更多
关键词 time-delay switched systems H∞ perfomance Lyapunov function linear matrix inequality
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Stability criteria for linear systems with multiple time-varying delays 被引量:1
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作者 Bugong XU(Laboratory of Real-Time Control Through Internet and Fieldbuses, College of Automation Science and Engineering, South China University of Technology, Guangzhou Guangdong 510640, China) 《控制理论与应用(英文版)》 EI 2003年第1期65-69,共5页
New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability ... New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406). 展开更多
关键词 STABILITY Delay-independent criteria Delay-dependent criteria linear time-delay systems Multiple time-varying delays
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New type of adaptive control for a class of distributed time-delay systems with adaptation regard to delay parameter 被引量:1
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作者 Lin Chai1, 2, Shumin Fei1, 2, Haiyan Jin1, 2, Ruimin Wang1, 2, and Yanhong Li1, 2 1. Key Laboratory of Measurement and Control of Complex Systems of Engineering, Southeast University, Nanjing 210096, P. R. China 2. School of Automation, Southeast University, Nanjing 210096, P. R. China 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第6期1054-1062,共9页
The problem on stabilization for the system with distributed delays is researched. The distributed time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A design method is propo... The problem on stabilization for the system with distributed delays is researched. The distributed time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A design method is proposed for a memory proportional and integral (PI) feedback controller with adaptation to distributed time-delay. The feedback controller with memory simultaneously contains the current state and the past distributed information of the addressed systems. The design for adaptation law to distributed delay is very concise. The controller can be derived by solving a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the design method. 展开更多
关键词 distributed delay linear matrix inequality (LMI) adaptive control time-delay systems memory PI feedback.
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Adaptive control for a class of discrete-time time-delay systems with regard to delay parameter 被引量:1
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作者 Chai Lin Cheng Ming +1 位作者 Fei Shumin Zhai Junyong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第1期159-167,共9页
The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our des... The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example. 展开更多
关键词 discrete-time time-delay systems adaptive control linear matrix inequality.
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