Distribution Of Delay Uncertain Neutral Systems With Robust H ¡Þ Control And Filter Design

Time delay phenomenon is often encountered in various practical systems, such as biological systems, chemical engineering systems, network control systems, neural networks, nuclear reactors, ship stabilization, population dynamic models, and so on. Time delay is frequently a source of instability and poor system performance. Therefore, the stability analysis and control problem for systems with time delays is of theoretical and practical significance. Neutral differential systems, as special time-delay systems, can describe many models of practical systems, such as chemical reactors, distributed networks, population ecology, lossless transmission lines, heat exchanges, and so on. In recent years, neutral systems has been widely investigated. According to the known conclusions at present, this paper investigates the problem of robust H∞control and filter for uncertain neutral systems with distributed time delays. Based on the Lyapunov function approach combined with linear matrix inequality (LMI) and free weighing matrix, a sufficient condition for the existence of such controller and filter is derived, and the corresponding controller and filter is obtained in terms of the feasible solution to the LMI.The main conclusions in this paper are as follows:(1)The problem of robust Hx control for uncertain neutral systems with dis-tributed time-varying delays. This paper considers the robust H∞control problem for a class of uncertain neutral systems with distributed time delays. The purpose is to design a full-order dynamic output feedback controller such that the closed-loop system is asymptotically stable and satisfies a prescribed H∞performance level, for all admissible parameter uncertainties and time delays. Based on the Lyapunov function approach combined with linear matrix inequality (LMI) and free weighing matrix, a sufficient condition for the existence of such controller is derived, and the corresponding robust Hx controller is obtained in terms of the feasible solution to the LMI. Finally, a numerical example is given to illustrate the feasibility and much less conservative of the proposed method.(2)A design of robust H∞filter for uncertain neutral systems with distributed time delays. In this paper, the design problem of robust H∞filtering for a class of uncertain neutral systems with distributed time delays is considered. The purpose is to design a full-order robust H∞filter such that the filtering error dynamic system is asymptotically stable and satisfies a prescribed Hx performance level, for all admis-sible parameter uncertainties and time delays. Based on the Lyapunov functional stability theory combined with linear matrix inequality (LMI), a sufficient condition for the existence of such filter is derived and a corresponding robust H∞filtering is obtained in term of the LMI feasible solutions. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.