H₂ state feedback controller design for continuous Markov jump linear systems with partly known information

Abstract

This article addresses the H ₂ control problem for continuous Markov jump linear systems with partly known information. The considered partly known transition probabilities cover the cases where the transition probabilities are exactly known, unknown and unknown but with known bounds. By decoupling the unknown transition probabilities from the Lyapunov matrices, new sufficient conditions for the H ₂ performance analysis of the considered systems are derived in terms of linear matrix inequalities (LMIs). Based on the result, an LMI-based method for designing H ₂ controllers is given. Two numerical examples are presented to illustrate the effectiveness of the proposed methods.

Keywords:

• H ₂ control
• partly known information
• transition probability matrix
• linear matrix inequality

Acknowledgements

This work was supported in part by the Funds for Creative Research Groups of China (No. 60821063), National 973 Programme of China (Grant No. 2009CB320604), the Funds of National Science of China (Grant No. 60974043), and the 111 Project (B08015), the Fundamental Research Funds for the Central Universities (No. N090604001, N090604002).