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

Abstract EN

The guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays.

The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound.

The associated cost function is of a quadratic summation form over the infinite horizon.

The nonlinear functions are assumed to satisfy sector-bounded conditions.

By introducing new Lyapunov-Krasovskii functionals and developing some new analysis techniques, sufficient conditions for the existence of guaranteed cost controllers are derived with respect to the given cost function.

Moreover, a convex optimization approach is applied to search for the optimal guaranteed cost controller by minimizing the guaranteed cost of the closed-loop system.

Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.