Robust H_∞Control For Nonlinear Uncertain Discrete-time Systems With Time-varying Delay

Time-delay is a widespread physical phenomenon in nature, and It exsists invarious practical engineering systems. Time-delay in a system is an important factor tocause the system instability, reduce system performance and induce system disorder.There are important theetical significance and engineering value to analysize andsynthesize time-delay daynamic systems. Therefore, in recent years the analysis andsynthesis on the time-delay systems have received much attention from the scholars.There have been a large number of effective results on the design of controllers, but thecontroller design on nonlinear systems with time-delay and uncertainty still need to beresearched further.In recent years, the control methods on the discrime-time systems with time delayhave developed fast. It should be noted that a series of new methods observablypromotes the development of uncertain discrime-time systems, such as, the descriptivemodel conversion method, a method of limiting quadratic tem and creating newinequality, a method of reserving a useful term as the upper bound of Lyapunovfunctional difference is set. Thus less conservativeness of the robust control method isarrived. The problem of robust H_∞control for uncertain unlinear discrete-time systemswith time-varying delay is discussed in this paper. Based on Lyapunov stability theoryand linear matrix inequalities, state feedback controller is constructed to ensure thesystem stability and meet some certain performance requirement by using adequateLyapunov functions. The main work in the paper is summarized as follows:(1) Firstly, the development of control theory, the research methods of robustcontrol and the stability analysis on the time delay systems are developed. On the otherhand, the necessary knowledge of the involved linear matrix inequalities (LMI) theoryand robustH_∞control are prepared.(2) Secondly, the research is largely focused on the Robust H_∞Control fornonlinear Discrete Systems with Time Delay and Uncertainty. Based on the Lyapunovfunctional method, and by resorting to the new technique for estimating the upperbound of the difference of the Lyapunov functional, a new less conservative sufficientcondition for the existence of a robust Hcontroller is obtained. Moreover, the cone complementary linearization procedure is employed to solve the nonconvex feasibilityproblem.(3) Finally, some programs are written using the LMI tool in MATLAB, andseveral numerical examples are presented to show the effectiveness and lessconservativeness of the proposed method. Meanwhile, the author gives some views onthe research on the robust control.