Decentralized Stabilization of Interconnected Systems with Time-varying Delays

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 an γ–level L2 –gain. A decentralized statefeedback stabilization scheme is designed such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed γ–level L2 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.