Stability analysis of large-scale interconnected switched systems with time delays

This paper studies the asymptotic stability of discrete-time large-scale interconnected switched systems with time delays. The system comprises many interconnected switched subsystems with several system modes. A total of three stability analysis conditions are given, all expressed as linear matrix inequalities. By leveraging the block-diagonal structure of system parameter matrices and the sparsity of the subsystem connection matrix, we first establish two stability analysis conditions that circumvent high-dimensional matrix inversion. In addition, we derive conditions that can be verified at the subsystem level. Compared with conventional computational approaches, the proposed conditions substantially reduce computational burden. Numerical simulation demonstrates the stability and efficiency of the proposed results, and a case study is introduced to further confirm this.