Robust H∞ dynamic output feedback control for nonlinear time-varying delay rectangular descriptor Markov jump systems

The robust H∞ dynamic output feedback (DOF) control for a class of nonlinear time-varying delay rectangular descriptor Markov jump systems (DMJSs) is discussed in this paper, there are no restrictions on the rows and columns of the differential matrix E. The rectangular DOF controller is designed to make the closed-loop system as square DMJSs. Firstly, by utilizing a mode-dependent and delay-dependent Lyapunov-Krasovskii (L-K) functional and implicit function theorem, sufficient conditions are given to guarantee that the augmented closed-loop systems are robust stochastically admissible with an H∞ performance and have unique solution simultaneously. Then based on certain matrix decoupling techniques, a new strict linear matrix inequality (LMI) sufficient condition for the existence of a rectangular DOF controller is obtained, and the controller is given. Finally, numerical examples are presented to verify the validity of the results.