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

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2 Author(s)
Mahmoud, M.S. ; Syst. Eng. Dept., King Fahd Univ. of Pet. & Miner., Dhahran, Saudi Arabia ; Al-Rayyah, A.Y.

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.

Published in:

Control Theory & Applications, IET  (Volume:4 ,  Issue: 1 )