Delay-Dependent Algebraic Riccati Equation to Stabilization of Networked Control Systems: Continuous-Time Case
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AbstractIn this paper, a delay-dependent algebraic Riccati equation (DARE) approach is developed to study the mean-square 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.
All Author(s) ListC. Tan, H. Zhang, Wing Shing Wong
Journal nameIEEE Transactions on Cybernetics
Volume Number48
Issue Number10
Pages2783 - 2794
LanguagesEnglish-United States

Last updated on 2021-13-05 at 01:38