Exponential stability analysis and L2-gain control synthesis for positive switched T-S fuzzy systems

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.