Robust stability of switched interconnected systems with multiple time delays and switching uncertainties

This study investigates the problem of robust stability in a class of switched interconnected systems that involve unstable modes, time-varying and continuously distributed state delays, as well as uncertainties in switching signal and system parameters. Switching uncertainties lead to fluctuations in both the prescribed switching instants and the nominal switching sequence, which significantly affect system stability. To address these challenges, two novel concepts are introduced: the composite switching signal and the generalized nominal switching signal. Additionally, a new index, referred to as the generalized mode-changing rate, is proposed. By utilizing these concepts and the new index, the average dwell time approach and the vector Lyapunov function method are integrated to derive sufficient conditions for ensuring the robust exponential stability of the system. Finally, a numerical example is provided to illustrate the effectiveness and applicability of the proposed theory.