Memory ℋ∞ control for continuous-time Markovian jump systems with time-varying delay and defective mode information

This paper investigates the problems of delay-dependent stability analysis and memory ℋ
_∞
controller synthesis for a class of continuous-time Markovian jump linear systems (MJLSs) via an input-output (IO) approach. The generality lies in that the exactly known, partially unknown and uncertain transition rates are simultaneously incorporated into the defective mode information. It is first shown that the original system with time-varying delay can be reformulated by a new IO model through a process of two-term approximation and the stability problem of the original system can be transformed into the scaled small gain (SSG) problem of the IO model. Then, based on a Markovian Lyapunov-Krasovskii formulation of SSG condition together with some convexification techniques, the stability analysis and state-feedbackℋ
_∞
controller synthesis conditions for the underlying MJLSs are formulated in terms of linear matrix inequalities. Simulation studies are provided to illustrate the effectiveness and superiority of the proposed analysis and design methods.