Adaptive control of systems with mismatched non-linearities and time-varying delays using state measurements

In this study, the authors develop a new delay-dependent adaptive control design method for a class of nominally linear continuous-time systems with time-varying delays and unknown non-linearities. The parameter uncertainties are convex-bounded and the unknown non-linearities are mismatched time-varying perturbations satisfying Lipschitz conditions in the state and delayed state. A new delay-dependent procedure is constructed based on a new form of Lyapunov-Krasovskii functional (LKF) together with a free-weighting matrix equation and the integral inequality. The feedback gains are determined by convex optimisation over linear matrix inequalities (LMIs) such that closed-loop adaptive controlled system is asymptotically stable. The theoretical developments are then extended to the case of polytopic uncertainties by deploying a parameter-dependent LKF. All the obtained results are tested on representative examples.