Observer-based dissipative control for Markovian jump systems via delta operators

This paper addresses the issue of observer-based dissipative control problem for a class of Markovian jump systems with random delay via delta operator approach. First, based on the construction of a novel Lyapunov functional together with the use of free-weighting matrix approach, a new set of sufficient conditions is established which ensures the stochastic asymptotic stability and dissipativity of the closed-loop augmented Markovian jump delta operator system. Next, the result is extended to design an observer-based state feedback dissipative control law such that the resulting closed-loop system is stochastically asymptotically stable with the desired dissipative performance index. Further, the existence of control laws is formulated in the form of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Also, the observer and control gains can be calculated by using the solutions of an obtained set of LMIs. It is worth pointing out that the dissipative control problem considered here includes the H∞ and passivity-based control problems as special cases. Finally, two numerical examples with simulation are presented to demonstrate the effectiveness of the obtained design technique.