Contraction Analysis for Discrete-Time Singular Nonlinear Switched Systems Via Their Surrogate Systems under Fully Known Switching Signals

We study the contraction analysis-a notion that ensures the system's trajectories converge exponentially to a certain trajectory-of discrete-time singular nonlinear switched systems under a fully known switching signal. A necessary and sufficient condition for the system to be contracting is provided via a single Lyapunov function approach, which is rather conservative due to the requirement of the existence of a common Lyapunov function for all subsystems. For a less conservative condition, a sufficient condition is then provided via a switched Lyapunov function approach. This approach does not require a common Lyapunov function for all subsystems, nevertheless, it requires that all subsystems are contracting. Finally, the study is complemented with illustrative examples of contracting switched systems.