Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov-Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.