Robust Stabilization And H_∞ Control Of Uncertain Discrete Time-Delay System

In recent years,discrete-time systems have attracted great attention because of their extensive engineering application background.In addition,time delay and uncertainty often exist in actual systems,and their existence will weaken the systems performance or make the systems unstable.Therefore,the research of discrete-time systems with time delay and uncertainty has very important theoretical significance and application value.This thesis studies the stabilization and controller design of uncertain nonlinear discrete-time systems with interval time-varying delays.The main contents and research results are as follows:Firstly,the problems of robust exponential stabilization and H_∞control for uncertain discrete-time nonlinear systems with interval time-varying delays are investigated.A state feedback controller is proposed.By constructing Lyapunov-krasovskii functional,using Wirtinger inequality,new summation inequality and free weight matrix technique,the criterion of robust exponential stabilization for uncertain discrete-time delay nonlinear systems based on state feedback control is established.Furthermore,the sufficient condition is proposed to ensure the corresponding closed-loop system is robust exponentially stable with disturbance rejection levelγ.The design method of H_∞controller gain matrix is given.Finally,the simulation example shows the effectiveness of the obtained results.Secondly,this thesis studies the robust H_∞finite-time stabilization of a class of discrete-time neural networks with time-varying delay.A static output feedback controller is designed.By using Lyapunov-Krasovskii functional theory,new summation inequality and Schur’s complement lemma,the criterion of robust H_∞finite-time stabilization for uncertain discrete-time delay neural networks based on static output feedback control is established.The design method of static output feedback control gain matrix is given.Then the dynamic output feedback controller is designed.A sufficient condition of robust H_∞finite-time stabilization for uncertain discrete-time delay neural networks based on dynamic output feedback control is obtained.The calculation method of dynamic output feedback control gain is given.When time delay is constant or the uncertainty is zero,the criteria of robust H_∞finite-time stabilization for discrete-time delay neural networks based on output feedback control are given respectively.Finally,a numerical example verifies the effectiveness of the proposed method.Finally,the problem of robust H_∞finite-time control for a class of uncertain discrete-time one-sided Lipschitz systems with interval time-varying delays is investigated.An observer-based controller is constructed.By selecting the appropriate Lyapunov-Krasovskii functional,using discrete Jensen’s inequality,reciprocally convex combination lemma and matrix inequality techniques,a sufficient condition of robust finite-time boundedness for the corresponding closed-loop system is given.Furthermore,the criterion is established to ensure the corresponding closed-loop system is robust H_∞finite-time bounded.The design methods of controller gain and observer gain are given respectively.When the time delay is constant or the uncertainty is zero,the sufficient conditions of robust H_∞finite-time boundedness for the corresponding closed-loop system are given respectively.Finally,a numerical example is given to verify the effectiveness of the proposed method.