Exponential stability analysis and [formula omitted]-gain control synthesis for positive switched T–S fuzzy systems

Abstract

In this paper, the problems of exponential stability analysis and weighted L2-gain control synthesis for positive switched T–S fuzzy systems are addressed. Firstly, by proposing a piecewise quadratic copositive Lyapunov function, a less conservative stability condition for positive switched T–S fuzzy systems is derived for the first time. Then, sufficient conditions for the positive switched T–S fuzzy system to be exponentially stable with a weighted L2-gain performance are obtained. Based on the obtained results, a state-feedback controller by the parallel distributed compensation scheme is designed to stabilize the positive switched T–S fuzzy system, while guaranteeing the prescribed weighted L2-gain performance and positivity in closed-loop. Finally, two numerical examples are presented to demonstrate the effectiveness of the obtained theoretical results.