Stability Analysis And Control Design For Several Discrete Systems With Interval Time-varying Delays

The problems of stability analysis and control design for discrete-time systems with internal time-varying delay are important research subjects in the field of discrete-time systems.In the dissertation,the stability analysis and controller design problem for several classes of nonlinear systems with time-varying delay are investigated.The main contributions of this dissertation are given as follows:Firstly,this paper considers the problem of the robust stability and stabi-lization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances.By constructing an appropri-ate Lyapunov-Krasovskii functional,and using linear matrix inequalities method,we establish some new delay-dependent robustly stochastic stability criteria for a class of uncertain discrete-time stochastic systems with interval time-varying delays.Robust feedback stabilization methods are provided based on state feed-back control.The new sufficient conditions for a class of uncertain discrete-time stochastic control systems with interval time-varying delays are established,under which the closed-loop system is robustly stochastically stable.The calculation method of the control gain is given.Numerical simulation examples are used to demonstrate the effectiveness and applicability of the obtained results.By intro-ducing some parameters ?1,?2,?1 and ?2 our method leads to less conservatism compared with the existing ones.Secondly,this paper deals with the problem of the global exponential sta-bility and for a class of uncertain discrete-time stochastic neural networks with interval time-varying delays.In the neural network model,the parameter uncer-tainties are norm-bounded.By using the linear matrix inequality method and the free-weighting matrix technique and constructing a new Lyapunov-Krasovskii functional,we establish new sufficient conditions to guarantee that the uncer-tain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square.Then,based on the state feed-back control law,some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established.The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems.Finally,numerical simulation examples illustrate the effectiveness of the theoretical results we have obtained.Finally,this paper investigate the problems of the stability analysis and H_?controller synthesis for discrete-time switched systems with interval time-varying delay and nonlinear disturbances.By constructing an appropriate Lyapunov-Krasovskii functional and using the linear matrix inequality method and the free-weighting matrix technique,the new delay-dependent robustly asymptotically stable criteria are established to guarantee that a class of uncertain discrete-time switched systems with interval time-varying delays is asymptotically stable.Fur-thermore,using the linear matrix inequality method and the free-weighting matrix technique,new sufficient conditions are proposed,which guarantee that discrete-time switched systems with interval time-varying delay and nonlinear disturbances are asymptotically stable with an H_? performance.The calculation method of the control gain is given.Finally,numerical simulation examples are given to illustrate the effectiveness of the theoretical results we have obtained.