Resilient decentralized stabilization of interconnected time-delay systems with polytopic uncertainties

Decentralized delay-dependent local stability and resilient feedback stabilization methods are developed for a class of linear interconnected continuous-time systems. The subsystems are time-delay plants which are subjected to convex-bounded parametric uncertainties and additive feedback gain perturbations while allowing time-varying delays to occur within the local subsystems and across the interconnections. The delay-dependent local stability conditions 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 by deploying an injection procedure such that every local subsystem is delay-dependent robustly asymptotically stable with an γ-level ℒ₂-gain. Resilient decentralized state-feedback stabilization schemes are designed, which takes into account additive gain perturbations 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 representative examples.