Mixed $H_2/H_{\infty}$ Control for Markov Jump Linear Systems with State and Mode-observation Delays.

In this paper, we study state-feedback control of Markov jump linear systems with state and mode-observation delays. We assume that the delay of the mode observation induced by the controllers follows an exponential distribution. We also introduce a time-varying state delay factor that is applied in the state-feedback controller. Our formulation provides a novel framework to analyze and design feedback control laws for the delayed Markov jump linear systems. We present a procedure to transform the closed-loop system into a standard Markov jump linear system with delays. Moreover, based on this transformation, we propose a set of Linear Matrix Inequalities (LMI) to design feedback gains for stabilization and mixed $H_2/H_{\infty}$ control. Numerical simulation is presented to illustrate the effectiveness of the theoretical results.