Invariance control for a class of cascade nonlinear systems

We consider the control of partially linear cascade systems using switching control of the states of the linear subsystem. We give suucient conditions under which feedback of the linear states with switching gains guarantees both exponential stability of the linear subsystem and positive invariance of a compact region in state space. Semi-global asymptotic stabilization follows under some additional conditions. Our design does not require linear growth assumptions on nonlinearities or ISS stability assumptions. Simulation results are presented showing the performance of the controller.