In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertaintie...In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter.展开更多
This paper deals with the iterative learning control (ILC) design for multiple-input multiple-output (MIMO),time-delay systems (TDS).Two feedback ILC schemes are considered using the so-called two-dimensional ...This paper deals with the iterative learning control (ILC) design for multiple-input multiple-output (MIMO),time-delay systems (TDS).Two feedback ILC schemes are considered using the so-called two-dimensional (2D) analysis approach.It shows that continuous-discrete 2D Roesser systems can be developed to describe the entire learning dynamics of both ILC schemes,based on which necessary and sufficient conditions for their stability can be provided.A numerical example is included to validate the theoretical analysis.展开更多
One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present ...One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present a parameter-dependent l 2-l ∞ performance criterion using a parameter-dependent Lyapunov function. Upon the conditions addressed, an improved parameter-dependent l 2-l ∞ performance criterion is established by the introduction of a slack variable, which exhibits a kind of decoupling between Lyapunov functions and system matrices. This kind of decoupling enables us to obtain more easily tractable conditions for analysis and synthesis problems. Then, the corresponding parameter-dependent state-feedback controller design is investigated upon these performance criteria, with sufficient conditions obtained for the existence of admissible controllers in terms of parameterized linear matrix inequalities. Finally, a numerical example is provided to illustrate the feasibility and advantage of the proposed controller design procedure.展开更多
L2 reading is not only an important channel for people to obtain information and knowledge,but also the main way for people to learn a foreign language.Reading information processing can be divided into controlled pro...L2 reading is not only an important channel for people to obtain information and knowledge,but also the main way for people to learn a foreign language.Reading information processing can be divided into controlled processing and automatic processing.Controlled information processing is a conscious and resource-intensive processing model,while automatic information processing is an unconscious and automatic processing model.This study investigates the characteristics and interactivity of controlled and automatic information processing in L2 reading,and explores the roles of controlled and automatic information processing strategies in improving L2 reading ability.The findings are as follows:(a)controlled and automatic information processing is interactive in L2 reading;and(b)the uses of controlled and automatic information processing strategies are beneficial to the improvement of the reading ability of L2 learners.This study has important theoretical and practical value in improving the efficiency of L2 reading teaching and learning.展开更多
The synthesis of new 4-imino-4H-chromeno[2,3-d]pyrimidin-3(5H)-amine in four steps including one step under microwave dielectric heating is reported. The structural identity of the synthesized compounds was establishe...The synthesis of new 4-imino-4H-chromeno[2,3-d]pyrimidin-3(5H)-amine in four steps including one step under microwave dielectric heating is reported. The structural identity of the synthesized compounds was established according to their spectroscopic analysis, such as FT-IR, NMR and mass spectroscopy. These new compounds were tested for their antiproliferative activities on seven representative human tumoral cell lines (Huh7 D12, Caco2, MDA-MB231, MDA-MB468, HCT116, PC3 and MCF7) and also on fibroblasts. Among them, only the compounds 6c showed micromolar cytotoxic activity on tumor cell lines (1.8 50 50 > 25 μM). Finally, in silico ADMET studies ware performed to investigate the possibility of using of the identified compound 6c as potential anti-tumor compound.展开更多
The exist researches of the magneto-rheological semi-active suspension(MSAS) control mainly focus on the design of control laws,which aim at obtaining an optimal control strategy to improve the ride comfort and handli...The exist researches of the magneto-rheological semi-active suspension(MSAS) control mainly focus on the design of control laws,which aim at obtaining an optimal control strategy to improve the ride comfort and handling stability.In the controller design,the stability of the MSAS system cannot be confirmed owing to the control input time delay considered little.In this paper,a quarter vehicle MSAS model with time-delay is built.Therefore,through formulating the sprung mass acceleration suitably as the optimization object,suspension deflection and tyre dynamic load and coulomb damping force as the constraint objects,with considering the control input time-delay,a delay-dependent state feedback H2/H∞ controller is designed.According to Lyapunov-Krasovskii functional theory,the sufficient conditions for asymptotic stability and the existence of delay-dependent H2/H∞ controller are obtained,and the controller design is transformed into the minimization problem for linear function through linear matrix inequality(LMI).Random road excitation simulations and experiments are carried out.The simulation and experiment results show that the design can preserve the closed-loop stability and achieve the performances for MSAS system in spite of the existence of the control input time-delay.The present study can provide an important basis and method for research on time-delay problem in MSAS and other chassis subsystems.展开更多
An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical react...An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone D<sub>O3</sub> and active atomic oxygen D<sub>O</sub> on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen D<sub>O</sub> was found to be more sensitive and important than that of ozone D<sub>O3</sub> on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .展开更多
Low-dimensional Bi2Fe4O9 nanosheets and microrods have been selectively prepared by a solvothermal method, from which the growth of the Bi2Fe4O9 crystals can be controlled by the variation of reaction conditions. Stru...Low-dimensional Bi2Fe4O9 nanosheets and microrods have been selectively prepared by a solvothermal method, from which the growth of the Bi2Fe4O9 crystals can be controlled by the variation of reaction conditions. Structure determination showed that the nanosheets are mainly exposed by {001} facets while the microrods are exposed by {110} facets. Ab- sorption spectra revealed that there are two bandgaps observed for both nanosheets (at 1.9 and 1.55 eV) and microrods (1.7 and 1.45 eV), and they both would be available for the sunlight photocatalysis e ciently due to the intensive absorption ability in a wide region. Photocatalytic investigation demonstrated that the overall photocatalytic performance of the microrods is prior to that of the nanosheets due to the variation of bandgaps and exposed facets. The present report provides a useful alternative strategy for the controlling growth of nanostructures and/or microcrystals besides the present demonstration of the Bi2Fe4O9 crystals with diflerent bandgaps and facets that would be able to tune the corresponding photocatalytic ability selectively.展开更多
A new type of 2-DOF(degree of freedom) magnetic levitation system for multi-DOF levitation is proposed. In this system, the force of permanent magnets are used for levitation and controlled by adjusting the reluctance...A new type of 2-DOF(degree of freedom) magnetic levitation system for multi-DOF levitation is proposed. In this system, the force of permanent magnets are used for levitation and controlled by adjusting the reluctance of the magnetic circuit. Using permanent magnets, the feature of this system is effective for saving energy and avoiding heat generation. First, the principle of the levitation system and typical reluctance control methods are described. Second, an experimental device based on the principle is introduced. Finally, the feasibility of this system is considered from linear control theory.展开更多
This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be ...This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.展开更多
This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New line...This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.展开更多
This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under contro...This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.展开更多
Vascular endothelial growth factor and its mimic peptide KLTWQELYQLKYKGI(QK)are widely used as the most potent angiogenic factors for the treatment of multiple ischemic diseases.However,conventional topical drug deliv...Vascular endothelial growth factor and its mimic peptide KLTWQELYQLKYKGI(QK)are widely used as the most potent angiogenic factors for the treatment of multiple ischemic diseases.However,conventional topical drug delivery often results in a burst release of the drug,leading to transient retention(inefficacy)and undesirable diffusion(toxicity)in vivo.Therefore,a drug delivery system that responds to changes in the microenvironment of tissue regeneration and controls vascular endothelial growth factor release is crucial to improve the treatment of ischemic stroke.Matrix metalloproteinase-2(MMP-2)is gradually upregulated after cerebral ischemia.Herein,vascular endothelial growth factor mimic peptide QK was self-assembled with MMP-2-cleaved peptide PLGLAG(TIMP)and customizable peptide amphiphilic(PA)molecules to construct nanofiber hydrogel PA-TIMP-QK.PA-TIMP-QK was found to control the delivery of QK by MMP-2 upregulation after cerebral ischemia/reperfusion and had a similar biological activity with vascular endothelial growth factor in vitro.The results indicated that PA-TIMP-QK promoted neuronal survival,restored local blood circulation,reduced blood-brain barrier permeability,and restored motor function.These findings suggest that the self-assembling nanofiber hydrogel PA-TIMP-QK may provide an intelligent drug delivery system that responds to the microenvironment and promotes regeneration and repair after cerebral ischemia/reperfusion injury.展开更多
Generalized H2 (GH2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov f...Generalized H2 (GH2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.展开更多
基金supported by the National Natural Science Foundation of China(61803085,61806052,U1713209)the Natural Science Foundation of Jiangsu Province of China(BK20180361)
文摘In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter.
基金Supported by National High Technology Research and Development Program of China (863 Program) (2006AA04Z183), National Natural Science Foundation of China (60621001, 60534010, 60572070, 60774048, 60728307), Program for Changjiang Scholars and Innovative Research Groups of China (60728307, 4031002)
基金supported by the National Natural Science Foundation of China(No.60727002,60774003,60921001,90916024)the COSTIND(No.A2120061303)the National 973 Program(No.2005CB321902)
文摘This paper deals with the iterative learning control (ILC) design for multiple-input multiple-output (MIMO),time-delay systems (TDS).Two feedback ILC schemes are considered using the so-called two-dimensional (2D) analysis approach.It shows that continuous-discrete 2D Roesser systems can be developed to describe the entire learning dynamics of both ILC schemes,based on which necessary and sufficient conditions for their stability can be provided.A numerical example is included to validate the theoretical analysis.
文摘One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present a parameter-dependent l 2-l ∞ performance criterion using a parameter-dependent Lyapunov function. Upon the conditions addressed, an improved parameter-dependent l 2-l ∞ performance criterion is established by the introduction of a slack variable, which exhibits a kind of decoupling between Lyapunov functions and system matrices. This kind of decoupling enables us to obtain more easily tractable conditions for analysis and synthesis problems. Then, the corresponding parameter-dependent state-feedback controller design is investigated upon these performance criteria, with sufficient conditions obtained for the existence of admissible controllers in terms of parameterized linear matrix inequalities. Finally, a numerical example is provided to illustrate the feasibility and advantage of the proposed controller design procedure.
文摘L2 reading is not only an important channel for people to obtain information and knowledge,but also the main way for people to learn a foreign language.Reading information processing can be divided into controlled processing and automatic processing.Controlled information processing is a conscious and resource-intensive processing model,while automatic information processing is an unconscious and automatic processing model.This study investigates the characteristics and interactivity of controlled and automatic information processing in L2 reading,and explores the roles of controlled and automatic information processing strategies in improving L2 reading ability.The findings are as follows:(a)controlled and automatic information processing is interactive in L2 reading;and(b)the uses of controlled and automatic information processing strategies are beneficial to the improvement of the reading ability of L2 learners.This study has important theoretical and practical value in improving the efficiency of L2 reading teaching and learning.
文摘The synthesis of new 4-imino-4H-chromeno[2,3-d]pyrimidin-3(5H)-amine in four steps including one step under microwave dielectric heating is reported. The structural identity of the synthesized compounds was established according to their spectroscopic analysis, such as FT-IR, NMR and mass spectroscopy. These new compounds were tested for their antiproliferative activities on seven representative human tumoral cell lines (Huh7 D12, Caco2, MDA-MB231, MDA-MB468, HCT116, PC3 and MCF7) and also on fibroblasts. Among them, only the compounds 6c showed micromolar cytotoxic activity on tumor cell lines (1.8 50 50 > 25 μM). Finally, in silico ADMET studies ware performed to investigate the possibility of using of the identified compound 6c as potential anti-tumor compound.
基金Supported by National High Technology Research and Development Program of China (863 Program) (2007AA04Z239) and National Natural Science Foundation of China (60621001, 60975060)
基金supported by National Natural Science Foundation of China (Grant No. 51075112,Grant No. 51175135)
文摘The exist researches of the magneto-rheological semi-active suspension(MSAS) control mainly focus on the design of control laws,which aim at obtaining an optimal control strategy to improve the ride comfort and handling stability.In the controller design,the stability of the MSAS system cannot be confirmed owing to the control input time delay considered little.In this paper,a quarter vehicle MSAS model with time-delay is built.Therefore,through formulating the sprung mass acceleration suitably as the optimization object,suspension deflection and tyre dynamic load and coulomb damping force as the constraint objects,with considering the control input time-delay,a delay-dependent state feedback H2/H∞ controller is designed.According to Lyapunov-Krasovskii functional theory,the sufficient conditions for asymptotic stability and the existence of delay-dependent H2/H∞ controller are obtained,and the controller design is transformed into the minimization problem for linear function through linear matrix inequality(LMI).Random road excitation simulations and experiments are carried out.The simulation and experiment results show that the design can preserve the closed-loop stability and achieve the performances for MSAS system in spite of the existence of the control input time-delay.The present study can provide an important basis and method for research on time-delay problem in MSAS and other chassis subsystems.
文摘An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone D<sub>O3</sub> and active atomic oxygen D<sub>O</sub> on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen D<sub>O</sub> was found to be more sensitive and important than that of ozone D<sub>O3</sub> on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .
基金This work was supported by the National Natu-ral Science Foundation of China (No.21571166 and No.51271173) and the National Basic Research Pro- gram of China (No.2012CB922001).
文摘Low-dimensional Bi2Fe4O9 nanosheets and microrods have been selectively prepared by a solvothermal method, from which the growth of the Bi2Fe4O9 crystals can be controlled by the variation of reaction conditions. Structure determination showed that the nanosheets are mainly exposed by {001} facets while the microrods are exposed by {110} facets. Ab- sorption spectra revealed that there are two bandgaps observed for both nanosheets (at 1.9 and 1.55 eV) and microrods (1.7 and 1.45 eV), and they both would be available for the sunlight photocatalysis e ciently due to the intensive absorption ability in a wide region. Photocatalytic investigation demonstrated that the overall photocatalytic performance of the microrods is prior to that of the nanosheets due to the variation of bandgaps and exposed facets. The present report provides a useful alternative strategy for the controlling growth of nanostructures and/or microcrystals besides the present demonstration of the Bi2Fe4O9 crystals with diflerent bandgaps and facets that would be able to tune the corresponding photocatalytic ability selectively.
文摘A new type of 2-DOF(degree of freedom) magnetic levitation system for multi-DOF levitation is proposed. In this system, the force of permanent magnets are used for levitation and controlled by adjusting the reluctance of the magnetic circuit. Using permanent magnets, the feature of this system is effective for saving energy and avoiding heat generation. First, the principle of the levitation system and typical reluctance control methods are described. Second, an experimental device based on the principle is introduced. Finally, the feasibility of this system is considered from linear control theory.
文摘This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.
文摘This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.
文摘This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.
基金supported by the Natural Science Foundation of Shandong Province,No.ZR2023MC168the National Natural Science Foundation of China,No.31670989the Key R&D Program of Shandong Province,No.2019GSF107037(all to CS).
文摘Vascular endothelial growth factor and its mimic peptide KLTWQELYQLKYKGI(QK)are widely used as the most potent angiogenic factors for the treatment of multiple ischemic diseases.However,conventional topical drug delivery often results in a burst release of the drug,leading to transient retention(inefficacy)and undesirable diffusion(toxicity)in vivo.Therefore,a drug delivery system that responds to changes in the microenvironment of tissue regeneration and controls vascular endothelial growth factor release is crucial to improve the treatment of ischemic stroke.Matrix metalloproteinase-2(MMP-2)is gradually upregulated after cerebral ischemia.Herein,vascular endothelial growth factor mimic peptide QK was self-assembled with MMP-2-cleaved peptide PLGLAG(TIMP)and customizable peptide amphiphilic(PA)molecules to construct nanofiber hydrogel PA-TIMP-QK.PA-TIMP-QK was found to control the delivery of QK by MMP-2 upregulation after cerebral ischemia/reperfusion and had a similar biological activity with vascular endothelial growth factor in vitro.The results indicated that PA-TIMP-QK promoted neuronal survival,restored local blood circulation,reduced blood-brain barrier permeability,and restored motor function.These findings suggest that the self-assembling nanofiber hydrogel PA-TIMP-QK may provide an intelligent drug delivery system that responds to the microenvironment and promotes regeneration and repair after cerebral ischemia/reperfusion injury.
文摘Generalized H2 (GH2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.