Delay-Dependent Algebraic Riccati Equation to Stabilization of Networked Control Systems: Continuous-Time Case.

Abstract

In this paper, a delay-dependent algebraic Riccati equation (DARE) approach is developed to study the meansquare stabilization problem for continuous-time networked control systems. Different from most previous studies that information transmission can be performed with zero delay and infinite precision, this paper presents a basic constraint that the designed control signal is transmitted over a delayed communication channel, where signal attenuation and transmission delay occur simultaneously. The innovative contributions of this paper are threefold. First, we propose a necessary and sufficient stabilizing condition in terms of a unique positive definite solution to a DARE with Q > 0 and R > 0. In accordance with this result, we derive the Lyapunov/spectrum stabilizing criterion. Second, we apply the operator spectrum theory to study the stabilizing solution to a more general DARE with Q ≥ 0 and R > 0. By defining a delay-dependent Lyapunov operator, we propose the existence theorem of the unique stabilizing solution. It is shown that the stabilizing solution, if it exists, is unique and coincides with a maximal solution. Third, as an application, we derive the explicit maximal allowable delay bound for a scalar system. To confirm the validity of our theoretic results, two illustrative examples are included in this paper.