On the robust stability of uncertain discrete-time networked control systems over fading channels

This paper addresses the problem of establishing robust stability in the mean square sense of uncertain discrete-time networked control systems over fading channels for all admissible uncertainties. It is supposed that the plant is connected to the controller in closed-loop via a fading channel which is modeled through noise processes in multiplicative form. The uncertainty is constrained into a convex bounded polytope and affects the plant whose coefficients are allowed to depend polynomially on the uncertainty. It is shown that robust stability of the uncertain closed-loop system in the mean square sense for all admissible uncertainties is equivalent to the existence of suitable Lyapunov functions with polynomial dependence on the uncertainty. It is also shown that a sufficient and necessary condition for establishing the existence of such Lyapunov functions can be obtained through convex optimization.