The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to...The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.展开更多
By means of matrix decomposition method a criterion is presented for the admissibility of T-S fuzzy descriptor system. Then, the problem of passivity control is studied for a kind of T-S fuzzy descriptor system with u...By means of matrix decomposition method a criterion is presented for the admissibility of T-S fuzzy descriptor system. Then, the problem of passivity control is studied for a kind of T-S fuzzy descriptor system with uncertain parameters, and sufficient conditions which make the closed-loop system admissible and strictly passive are obtained based on linear matrix inequality (LMI). The nonstrict LMIs restricted conditions which characterize the descriptor system are transformed into strict ones, so testing admissibility and passivity of the system can be finished simultaneously. The design scheme of state feedback controller is also obtained. Finally, a numerical example is given to show the validity and feasibility of the proposed approach.展开更多
This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model ...This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fu...This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.61004038)
文摘The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.
基金Supported by National Natural Science Foundation of P. R, China (60574011)the Distinguished Teacher Funds of Liaoning Universities (124210)the Key Laboratory Funds of Liaoning Universities of Intelligent Control Theory and Applications
文摘By means of matrix decomposition method a criterion is presented for the admissibility of T-S fuzzy descriptor system. Then, the problem of passivity control is studied for a kind of T-S fuzzy descriptor system with uncertain parameters, and sufficient conditions which make the closed-loop system admissible and strictly passive are obtained based on linear matrix inequality (LMI). The nonstrict LMIs restricted conditions which characterize the descriptor system are transformed into strict ones, so testing admissibility and passivity of the system can be finished simultaneously. The design scheme of state feedback controller is also obtained. Finally, a numerical example is given to show the validity and feasibility of the proposed approach.
基金Supported by National Natural Science Foundation of China （50977008, 60904017, 60774048, 60728307）, the Funds for Creative Research Groups of China （60521003）, the Program for Cheung Kong Scholars and Innovative Research Team in University （IRT0421）, and the 111 Project （B08015）, National High Technology Research and Development Program of China （863 Program） （2006AA04Z183）
文摘This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
基金This research was supported by the National Natural Science Foundation of China under Grant No.61903167.
文摘This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.
