<inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{2}$</tex-math> </inline-formula>– <inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{\infty }$</tex-math> </inline-formula> Output Feedback Controller Design for Fuzzy Systems Over Switching Parameters

Abstract

This paper focuses on the problem of $\mathcal {L}_{2}$ – $\mathcal {L}_{\infty }$ dynamic output feedback controller (DOFC) design for nonlinear switched systems with nonlinear perturbations in the Takagi–Sugeno fuzzy framework. First, the average dwell time approach is used to stabilize a nonlinear switched system exponentially under an arbitrary switching law. Then, based on the technique of piecewise Lyapunov functions, a fuzzy-rule-dependent DOFC is designed to ensure that the overall closed-loop system is exponentially stable with a weighted $\mathcal {L}_{2}$ – $\mathcal {L}_{\infty }$ performance level $\left(\gamma,\alpha \right)$ . The solvability condition for the desired DOFC is derived using a linearization technique. It is shown that the controller parameters can be obtained as solutions to a set of strict linear matrix inequalities that are numerically solvable with available standard software. Finally, two simulation examples illustrate effectiveness of the developed technique, including cognitive-radio systems.