Asynchronous H∞ fuzzy control for a class of switched nonlinear systems via switching fuzzy Lyapunov function approach

• The previous work studied the H∞H∞ asynchronous control problem of switched systems mainly focused on the switched linear systems. We use the T–S fuzzy model to study the H∞H∞ asynchronous control problem of the continuous-time switched nonlinear systems. Furthermore, our work can also reduce to study the H∞H∞ asynchronous control problem of continuous-time switched linear systems.
• In order to further reduce the conservativeness resulted from the nonlinearity and the common Lyapunov functions approach, we propose the switching fuzzy Lyapunov functions approach, and this approach can also apply to study other switched nonlinear systems.
• The mode-dependent average dwell time (MDADT) switching scheme is used in our study, which can further reduce the conservativeness of results.

This paper addresses the problem of H∞H∞ control for a class of continuous-time switched nonlinear systems via switching fuzzy Lyapunov functions (FLFs). The asynchronous switching is also considered in this paper, where “asynchronous” means that the switching of the controllers to be designed has a lag to the switching of the system models. The Takagi–Sugeno (T–S) fuzzy model is used here to approximate each nonlinear subsystem of the switched nonlinear systems. By using mode-dependent average dwell time (MDADT) techniques, we obtain stability conditions for the open-loop switched nonlinear systems and stabilization conditions with H∞H∞ performance for the closed-loop switched nonlinear systems. The desired H∞H∞ controller can be constructed by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples illustrate the utility and advantage of the proposed method.