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 transmission delay and data packet dropout may occur simultaneously. The stabilization for such NCSs remains challenging because of the fundamental difficulty in stochastic control. The contributions of this paper are threefold. First, we present two different necessary and sufficient stabilizing conditions in terms of the unique positive solution to delay-dependent algebraic Riccati equation (DARE) or delay-dependent Lyapunov equation (DLE). Second, the maximum packet dropout rate can be calculated with a proposed optimization algorithm. Third, the stabilizing solution to developed DARE is investigated for its existence and uniqueness. We show the existence condition in terms of the Lyapunov operator and the unobservable mean-square eigenvalue, under which the general DARE has a unique stabilizing solution.