L 1 control for positive Markovian jump systems with partly known transition rates

Abstract

This paper deals with the problem of L1 control for positive Markovian jump systems with partly known transition rates. First, by constructing an appropriate linear co-positive type Lyapunov-Krasovskii function, stochastic stability for the underlying system is discussed. Then, the L1-gain performance is analyzed. Based on the results obtained, an effective method is proposed for the design of state feedback controller. All the proposed conditions are derived to ensure that the closed-loop Markovian jump system positive and stochastically stable with L1-gain performance in linear programming. Finally, an example is given to demonstrate the validity of the main results.