Stabilising nonlinear systems with time-varying delays by new parametrised method

This paper establishes new robust delay-dependent stability and stabilisation methods for a class of nonlinear continuous-time systems with time-varying delays. The nonlinearities are unknown time-varying perturbations satisfying Lipschitz conditions in the state and the delayed-state. An appropriate Lyapunov functional is constructed and delay-dependent stability analysis is performed to characterise Linear Matrix Inequalities (LMIs)-based conditions under which the nominally-linear delay system is robustly asymptotically stable with an γ-level L2-gain. Then we design delay-dependent feedback stabilisation schemes: a static one based on state (delayed-satte)-measurements and a dynamic one based on observer-based output feedback. In all schemes, the closed-loop feedback system enjoys the delay-dependent asymptotic stability with a prescribed γ-level L2-gain. The feedback gains are determined by convex optimisation over LMIs and all the developed results are tested on a representative example.