On Incremental Stability of Interconnected Switched Systems

In this letter, the incremental stability of interconnected systems is discussed. In particular, we consider an interconnection of switched nonlinear systems. The incremental stability of the switched interconnected system is a stronger property as compared to conventional stability. Guaranteeing such a notion of stability for an overall interconnected nonlinear system is challenging, even if individual subsystems are incrementally stable. Here, preserving incremental stability for the interconnection is ensured with a set of sufficient conditions. Contraction theory is used as a tool to achieve incremental convergence. For the feedback interconnection, the small gain characterisation is presented for the overall system's incremental stability. The results are derived for a special case of feedback, i.e., cascade interconnection. Matrix-measure-based conditions are presented, which are computationally tractable. Two numerical examples are demonstrated and supported with simulation results to verify the theoretical claims.