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Decentralized stabilization of interconnected systems with time-varying delays. (English) Zbl 1187.93002

Summary: Decentralized delay-dependent stability and stabilization methods are developed for a class of linear interconnected continuous-time systems. The subsystems are time-delay plants subjected to convex-bounded parametric uncertainties and the interconnections are time-delay couplings. The delay-dependent dynamics are established at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional. We characterize decentralized Linear Matrix Inequalities (LMIs)-based delay-dependent stability conditions such that every local subsystem of the linear interconnected delay system is robustly asymptotically stable with a \(\gamma\)-level \({\mathcal L}_2\)-gain. A decentralized state feedback stabilization scheme is designed such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed \(\gamma\)-level \({\mathcal L}_2\) gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example.

MSC:

93A14 Decentralized systems
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
93D20 Asymptotic stability in control theory
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