Nonlinear Singular Switched Systems in Discrete-Time: Solution Theory and Incremental Stability Under Restricted Switching Signals

In this article the solvability analysis of discrete-time nonlinear singular switched systems with restricted switching signals is studied. We provide necessary and sufficient conditions for the solvability analysis under fixed switching signals and fixed mode sequences. The so-called surrogate systems (ordinary systems that have the equivalent behavior to the original switched systems) are introduced for solvable switched systems. Incremental stability, which ensures that all solution trajectories converge with each other, is then studied by utilizing these surrogate systems. Sufficient (and necessary) conditions are provided for this stability analysis using single and switched Lyapunov function approaches.