Exponential stability of switched nonlinear cascade systems with time-delay

The exponential stability of switched nonlinear cascade systems with time-delay is studied in this paper. By using the average dwell-time method and piecewise Lyapunov function approach, the sufficient conditions that make the switched systems exponentially stable are obtained. And the switching law is designed, which included the average dwell-time of the switched systems. Meanwhile, systems with uncertainties are also considered. The result can be described in the form of LMI, which can be evaluated easily. Finally, a simulation example is given to illustrate the validity of the result.