Mean square stability of continuous-time delay-difference systems with Markovian switching

In this paper, the stability analysis problem of continuous-time delay-difference systems with Markovian switching is studied. Firstly, a condition based on linear matrix inequalities (LMIs) for the transformation of mean square (Formula presented.) -exponential stability into mean square exponential stability and a Lyapunov-Krasovskii functional (LKF) stability theorem to test the mean square (Formula presented.) -exponential stability with a guaranteed convergence rate are established. Then, for a class of particular systems with both point delays and distributed delays having exponential integral kernels, less conservative stability conditions based on LMIs are established by constructing a mode-dependent LKF. Finally, some numerical examples are worked out to illustrate the effectiveness and superiority of the theoretical results.