Stabilization of primal and dual positive switched systems and application to T-S fuzzy systems

This paper is concerned with stabilization of primal and dual positive switched systems and T-S fuzzy systems. State-feedback stabilization of primal and dual positive switched systems is first addressed. All present conditions can be described via linear programming. An implementable algorithm is given to increase the feasibility of the linear programming problems. It is shown that, a switched linear copositive Lyapunov function of dual positive switched systems can be established, and the controller of the dual systems can be also used to stabilize the primal systems. Then, the proposed design is applied to primal and dual positive T-S fuzzy systems. A fuzzy linear copositive Lyapunov function for dual positive T-S fuzzy systems is constructed, and stabilization of primal and dual positive T-S fuzzy systems is solved. The results obtained in this paper reduce the conservatism of existing results on positive switched systems and T-S fuzzy systems based on common linear copositive Lyapunov functions. Two illustrative examples verify the findings of theory.

1 Introduction

Positive systems are an important class of systems that arises frequently in many practical applications, for instance, biology, communications, economics, population level, and in other fields. Since these practical systems mentioned above involve quantities that are intrinsically nonnegative, the positivity assumption is a natural one. Past years have witnessed an increasing interest in the class of systems. More information about this class of systems can be found in [1]–[4].