Stability Analysis And Filter Design For Two Class Of Lurie Systems With Time-delays

Lurie control system has always been an indispensable part of nonlinear control system, it’snamed by Lurie studying nonlinear system model in1944. This system can be simplified as a linearand a nonlinear system. The linear system is described as a accurate and stable system while thenonlinear system in a sector constituted by two lines. This paper deal with the absolute stability, filterdesign problem for several Lurie systems. The main content of this paper contains three parts:In the first part, the absolute stability problem for a neutral Lurie system with mixed delayhas been investigated. Firstly, the discrete delay is divided into multiple segments. By using delaydecomposition approach, the absolute stability problem is solved by constructing a new Lyapunov-Krasovskii function, and the result is constrained by infinite sector and finite sector respectively.Then, this paper consider the further study of the absolute stability of nonlinear uncertain neutralLurie system.The second part consider the absolute stability of a class of neutral Lurie system with sector-infinity and time-varying delays. In particularly, the neutral dalay is a constant and the state delay isa time-varying delay bounded in an unknown interval. By dividing the interval into pieces, The NewLyapunov-Krasovskii functions are obtained. Finally, we get the absolute stability condition usingLebniz-Newton function and free weight matrix in infinite condition. Since the method based on theintegral inequality and the free weighting matrix. It is less conservative than previous methods.The third part focus on the∞design for a class of Lurie system with time-varying delayin finite sector. The method is based on T-S fuzzy model and we get a delay-dependent conditionusing linear matrix inequality. By involving a free weight matrix, new delay-dependent Lyapunov-Krasovskii function is created for the error system. In order to reduce conservatism created by thecoupling variable, a matrix decoupling approach is used.At the end of each part, Examples are given to show the feasibility of our methods.