Robust exponential stability and L2-gain for switched discrete-time nonlinear cascade systems

The robust exponential stability and L₂-gain for a class of switched discrete-time nonlinear cascade systems are considered in this paper. Firstly, the exponential stability for switched discrete-time nonlinear cascade systems affected by norm-bounded time-varying uncertainties is studied. With an inequality of the inverse matrix and other matrix inequalities, the uncertainties in systems can be subtly handled. Using the average dwell-time method and piecewise Lyapunov function approach, a sufficient condition of the robust exponential stability for switched systems in this case is given. Then, the L₂-gain of switched discrete-time nonlinear cascade systems with the externally disturbed input is analyzed. The sufficient conditions of the exponential stability and L₂-gain for switched nonlinear systems are obtained under the designed switching law. Finally, the simulations are given to show the validity of the results.