Dissipativity analysis and design for uncertain Markovian jump systems with time-varying delays

This paper deals with the problems of dissipativity analysis and dissipativity-based controller design for Markovian jump systems with both time-varying delays and norm-bounded parametric uncertainties. Improved delay-dependent conditions for the system concerned to be strictly dissipative are established by using a mode-dependent Lyapunov–Krasovskii functional and introducing some slack variables. These conditions are expressed by means of linear matrix inequalities (LMIs) which are easy to check. It is also shown that these conditions are less conservative than those obtained by using the existing methods. The dissipativity synthesis problem is considered and on the basis of the obtained dissipativity conditions, both the state-feedback and dynamic output-feedback controllers are designed to guarantee the strict dissipativity of the closed-loop systems. Numerical examples are provided to demonstrate the utility of the developed methods.