Stabilization of networked control systems with both network-induced delay and packet dropout

This paper is concerned with the mean-square stabilization problem for discrete-time networked control systems (NCSs). It is assumed that control signal is sent to plant over a lossy communication channel, where network-induced delay and packet dropout occur simultaneously. A necessary and sufficient stabilizing condition is developed in terms of the unique positive-definite solutions to some coupled algebraic Riccati equations (CAREs). The contributions of this paper are twofold. First, an existence theorem of the maximum packet dropout rate is proposed. Second, for one-dimensional single-input system and the decoupled multi-input system, it is shown that the NCS is stabilizable iff the network-induced delay and the packet dropout rate satisfy some simple algebraic inequalities. If the network-induced delay is known a priori, the maximum packet dropout rate is given explicitly in terms of network-induced delay and unstable eigenvalues of the system matrix. If the packet dropout rate is known a priori, the maximum allowable delay bound is also given explicitly.