Almost sure stability and stabilization of variable dual switching time-delay systems

This article is concerned with the exponential almost sure stability and stabilization of variable dual switching time-delay systems (VDSTDSs). Firstly, a novel state-dependent switching strategy named minimum state expectation (MSE) is proposed. Under the MSE switching strategy, the VDSTDSs switch to the next Markov jump subsystem with a smaller state expectation. This switching approach fully considers the interaction between deterministic and stochastic switching signals, which is more general for VDSTDSs than dwell time, average dwell time, and persistent dwell time switching. Subsequently, considering the complex switching dynamics and delay dynamics, a mode-dependent Lyapunov-Krasovskii functional (LKF) that contains an exponential term and a triple integral term is constructed to balance the conservativeness and computational complexity. The generalized free-matrix-based integral inequality is used to estimate the integral term in the LKF derivative. Sufficient conditions are established in the form of linear matrix inequalities to ensure the delay-dependent exponential almost sure stability and stabilization of the VDSTDSs. Finally, a numerical example and a multi-loop networked control system model are provided to illustrate the effectiveness and applicability of the proposed methods.