Exponential stability for switched discrete-time nonlinear cascade systems with time-varying delays

The exponential stability for a class of switched discrete-time nonlinear cascade systems with time-varying delays is discussed in this paper. By converting the discrete cascade systems with time-varying delays into switched systems, a new system form is presented. To solve the problem of stability, the average dwell-time method and piecewise Lyapunov function approach are applied. Also, the exponential stability for the switched discrete-time nonlinear systems with time-varying delays affected by norm-bounded time-varying uncertainties is considered. Based on the conditions we have obtained, the switched system can be exponentially stable under the designed switching law. Finally, two examples are given to illustrate the validity of the results.