Improved stability and stabilization approach to linear interconnected time-delay systems

In this paper, we investigate the problems of delay-dependent analysis and state-feedback synthesis for a class of linear continuous-time interconnected systems with time-varying delays. An augmented Lyapunov functional is properly constructed for the individual subsystems and an improved free-weighting method is deployed to exhibit the delay-dependent dynamics. Delay-dependent stability analysis is then performed to develop linear matrix inequalities (LMIs)-based conditions under which the family of linear delay subsystems is asymptotically stable with a γ-level L2-gain for the nominal model. Extension to systems with convex bounded parameter uncertainties in all system matrices is also provided. All the required numerical computations are performed on the subsystem level. By delay-dependent stabilization, we design a family of local state-feedback schemes to guarantee that the closed-loop subsystem enjoys the delay-dependent asymptotic stability with a prescribed γ-level L2-gain. The developed results are tested on a representative example to illustrate the theoretical developments.