Stability Analysis for Dual Switching Linear Continuous-Time Systems

In this paper, we are dedicated to investigate the globally asymptotical stability almost surely (GAS a. s.) and almost surely exponential stability (ES a. s.) of dual switching linear continuous-time systems based on the probability analysis method and Multi-Lyapunov function. To extend the results already obtained and to investigate some new aspects of such systems, our main contributions in this paper are: i) Switching signal design, i.e., the smallest expected value is selected as the deterministic switching signal. ii) Sufficient conditions of the (GAS a. s.) and (ES a. s) for the dual switching linear continuous-time systems. Different from previous work, which is a special case of our study, the transition rate matrix for the random Markov process in our study is not fixed, but varies when a deterministic switching takes place.