A less conservative criterion for exponential mean-square stability of networked control systems with stochastic packet dropouts

This paper is concerned with the modeling and the control of networked control systems (NCSs) with stochastic packet dropout. In order to facilitate the technical description, network-induced time delay is assumed to be ignorable.The closed-loop NCS with stochastic packet dropout is modeled as a continuous-time system with time-varying delays and stochastic parameters. By utilizing the Lyapunov-Krasovskii functional method, the integral inequality lemma and the Gronwall-Bellman lemma, a less conservative criterion for exponential mean-square stability of NCS with stochastic packet dropout is presented in the form of nonlinear matrix inequalities. Meanwhile, the state feedback gain matrix is provided based on solving a linear matrix inequality (LMI). Moreover, the state feedback gain matrix is obtained by solving a linear matrix inequality (LMI). Based on the solvability of this LMI, the allowable upper bound of continuous packet dropouts is determined, from which the maximum allowable time interval (MATI) can also be derived. Finally, a numerical example is given to demonstrate the effectiveness of our results.