The previous work studied the H_∞$H_{\infty }$ asynchronous control problem of switched systems mainly focused on the switched linear systems. We use the T–S fuzzy model to study the H_∞$H_{\infty }$ asynchronous control problem of the continuous-time switched nonlinear systems. Furthermore, our work can also reduce to study the H_∞$H_{\infty }$ 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.