Necessary and sufficient stabilizing conditions for networked control systems with simultaneous transmission delay and packet dropout

This paper investigates the mean-square stabilization problem for discrete-time networked control systems (NCSs). Different from most previous studies, we assume that transmission delay and packet dropout may occur simultaneously. The stabilization problem for such NCSs remains challenging because of the fundamental difficulty of stochastic control. The contributions of this paper are twofold. First, we present a necessary and sufficient condition for stabilizing the NCSs in terms of the unique positive solution to a specified algebraic equation. It is also shown that the NCS is stabilizable iff the generalized Lyapunov equation has a positive solution, which is in accordance with the classical result for a delay-free system. Second, we propose an optimization algorithm for computing the maximum packet dropout rate. The key technique adopted in this paper involves the Riccati-ZXL equation established in our earlier work.