Guaranteed Cost Control Of Liner Discrete-time Systems With Nonlinear State Saturation Constrains

Saturation phenomenon generally exists in the biological, engineering and social economic practical systems. State saturation constraints will have a great influence on the performance of the control system, even lead to instability of the stable sys-tem. Therefore, research on saturation constraint of the control system has impor-tant theoretical and practical significance. This article talks about the guaranteed cost control problem of the discrete system subject to saturation nonlincaritics.First, the problem of designing guaranteed cost controllers for a class of linear discrete-time systems with saturation nonlinearities is considered. Together with a given quadratic performance index, a sufficient condition for the existence of state feedback guaranteed cost controller is derived on basis of Lyapunov stability theory and linear matrix inequalities. Furthermore, we give an approach for getting guar-anteed cost controller law via linear matrix inequalities method. Finally, an example is given to demonstrate the efficiency of the proposed approach.Secend, the problem of designing a guaranteed cost state feedback control law for a class of uncertain linear discrete time-delay systems with saturation constraint, is studied. Then, given a sufficient condition for the closed-loop system is robustly stable and the upper bound index has a certain cost under state feedback control, and thus puts forward cost upper bound index of state feedback controller is as small as possible that is the optimal guaranteed cost state feedback controller design method. A numerical example demonstrates the validity of the approach proposed.Third, the robust asymptotic stability problem for a discrete-time systems with time-varying delay subject to saturation nonlinearities is adressed in this paper.The purpose is to design a state—feedback controller such that the resulting closed-loop system is robustly stable. Together with a given quadratic performance index, a sufficient condition for the existence of robust stability controller is derived on basis of Lyapunov stability theory. Furthermore, we getting robust stability controller via...