Nonlinear Switched Systems with State Dependent Dwell-Time

The asymptotic convergence of nonlinear switched systems in the presence of disturbances is studied in this paper. The system switches among a family of integral input-to-state stable systems. The time between two consecutive switchings is not less than a value τD. This dwell-time τD is allowed to take different values according to a function whose argument is the state of the system at the switching times. We propose a dwelltime function which depends on the comparison functions which characterize the integral input-to-state stability and guarantees the state of the switched system to converge to zero under the action of disturbances with “bounded energy”. The main feature of the analysis is that it does not rely on the property that the switching stops in finite time. The two important cases of locally exponentially stable and feedforward systems are analyzed in detail.