  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.
