Efficient parameterisation to stability and feedback synthesis of linear time-delay systems

In this study, we provide efficient solution to the problems of delay-dependent analysis and feedback synthesis for a class of linear continuous-time systems with time-varying delays. An augmented Lyapunov functional is properly constructed 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 linear delay system is asymptotically stable with an gamma-level L₂ gain. The superiority of the developed method in comparison with other existing methods is established. By delay-dependent feedback synthesis, we design state-feedback and dynamic output-feedback schemes to guarantee that the closed-loop system enjoys the delay-dependent asymptotic stability with a prescribed gamma-level L₂ gain. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples.