New characterisations of positive realness and static output feedback control of discrete-time systems

Abstract

This article is concerned with the problems of positive real analysis and control synthesis for discrete-time systems. New linear matrix inequality (LMI) characterisations of positive realness are derived, which enable one to check the positive realness by using parameter-dependent Lyapunov function. The relationship between the proposed characterisations and the existing ones are clarified, which shows that our new results are of less conservatism for characterising the positive realness of discrete-time systems with polytopic uncertainty. In addition, sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities. Numerical examples are included for illustration.

Keywords:

• positive realness
• parameter-dependent Lyapunov function
• static output feedback
• linear matrix inequality (LMI)

Acknowledgements

This work is supported in part by Program for New Century Excellent Talents in University (NCET-04-0283), the Funds for Creative Research Groups of China (No. 60521003), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0421), the State Key Program of National Natural Science of China (Grant No. 60534010), the Funds of National Science of China (Grant No. 60804024, 60674021) and the Funds of PhD program of MOE, China (Grant No. 20060145019), the 111 Project (B08015).