Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays

摘要

The guaranteed cost control problem is investigatedfor a class of nonlinear discrete-time systems with Markovianjumping parameters and mixed time delays. The mixed time delaysinvolved consist of both the mode-dependent discrete delay and thedistributed delay with mode-dependent lower bound. The associatedcost function is of a quadratic summation form over the infinitehorizon. The nonlinear functions are assumed to satisfysector-bounded conditions. By introducing new Lyapunov-Krasovskiifunctionals and developing some new analysis techniques,sufficient conditions for the existence of guaranteed costcontrollers are derived with respect to the given cost function. Moreover, a convex optimization approach is applied to search forthe optimal guaranteed cost controller by minimizing theguaranteed cost of the closed-loop system. Numerical simulation isfurther carried out to demonstrate the effectiveness of theproposed methods.