Stability Analysis And Output Feedback Controller Design For T-S Fuzzy Time-Delay Disturbance Systems

In practice,the time-delays are often encountered in various systems,such as the economics,population,biology,metallurgy,aerospace and so on.Due to the important practical application background of the time-delay system,it has attracted much more attention from scholars at home and abroad.Time-delays phenomenon is one of the main reasons leading to the instability,oscillation and even system performance degradation.Thus,it is of great practical significance to carry out the stability analysis and the controller design for the time-delay system.The stability analysis and controller design for the time-delay systems have important practical significance.Based on fuzzy control theory,the new stability criteria are studied in the linear system with time delay,and the output feedback controllers are designed for the T-S fuzzy time-delay systems and type-2fuzzy time-delay system.The main research works are presented as follows:(1)The new stability criterions for the asymptotic stability of the linear time-delay systems are investigated via the integral inequalities and Jensen inequalities.The linear system with known constant time delay and the linear system with unknown time varying delay are both considered.Based on the integral inequalities and Jensen inequalities,the delay-dependent Lyapunov-Krasovskii function is introduced and the stability conditions of the linear systems are presented.Two classes of delay-dependent LMIs are derived for the linear system with known constant time-delay and the linear system with unknown time-varying delay,respectively.Compared with previous works,the computation complexity is reduced,the larger feasible solution region and less conservative results are obtained.(2)The new fuzzy dynamic output feedback control method is proposed for a class of T-S fuzzy systems with multiple time-varying delays and external disturbances.The T-S fuzzy dynamic output feedback controller is designed based on the T-S fuzzy model.By introducing the linear integral fuzzy Lyapunov-Krasovskii function,the stability conditions in terms of LMIs are derived for the system,and the boundary information of the fuzzy membership function is considered in the stability analysis.Both the multiple time-varying time-delays and external disturbance are considered in the system model.The T-S fuzzy dynamic output feedback controller and the T-S fuzzy system share the same number of fuzzy rules,but different membership functions to relax the design conditions.The linear integral fuzzy Lyapunov-Krasovskii function is introduced and the boundary information of membership function is considered to obtain the less conservative stability results.(3)The T-S fuzzy dynamic output feedback control method is proposed for a class of uncertain T-S fuzzy systems with mixed time-varying delays and uncertainties.The T-S fuzzy dynamic output feedback controller is designed by employing the descriptor redundancy approach.The non-quadratic stability conditions in terms of LMIs are derived by introducing the descriptor redundancy approach and non-quadratic fuzzy Lyapunov-Krasovskii function,and the closed-loop system is asymptotically stable and state variables converge to an adjustable bounded region.The design conditions are relaxed because of the proposed dynamic output feedback controller.By introducing the descriptor redundancy approach and non-quadratic fuzzy Lyapunov-Krasovskii function,the numerous crossing terms in the LMIs are avoided in the system design.(4)The T-S fuzzy dynamic output feedback control method is proposed for a class of discrete-time T-S fuzzy systems with time-varying delays and unmatched disturbances.Based on the stochastic system theory and Bernoulli probability distribution,the T-S fuzzy dynamic output feedback controller is designed for the discrete-time T-S fuzzy system with time-varying delay and unmatched disturbance.The H_?performance analysis is presented,and the cone complementarity linearization algorithm is employed in the stability analysis to solve the non-convex problem caused by the basis-dependent LMIs.The proposed controller is effective in this paper and the flexibility of the controller design is enhanced because of the cone complementarity linearization algorithm.(5)The H_?stability analysis and interval type-2 T-S fuzzy dynamic output feedback control method is proposed for a class of interval type-2 T-S fuzzy systems with time-varying delays and external disturbance.The interval type-2 T-S fuzzy dynamic output feedback controller is designed by employing the interval type-2 T-S fuzzy model,such that the design conditions are relaxed and design flexibility is enhanced.The closed-loop system is described as a descriptor system by employing the descriptor redundancy approach.Two classes of stability conditions are derived by introducing the Lyapunov-Krasovskii function,such that the closed-loop system is asymptotically stable and the prescribed H_?performance is achieved.The less conservative stability criterions are extended to a finite set of LMIs constraints and the LMIs are solved effectively.