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

Authors: Magdi S. Mahmoud, Ali Y. Al-Rayyah

Addresses: Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. 985, Dhahran 31261, Saudi Arabia. ' Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. 985, Dhahran 31261, Saudi Arabia

Abstract: 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.

Keywords: nonlinear systems; time-delay systems; delay-dependent stability; feedback stabilisation; LMI; linear matrix inequality; continuous-time systems; time-varying delays; convex optimisation.

DOI: 10.1504/IJSCC.2011.039228

International Journal of Systems, Control and Communications, 2011 Vol.3 No.1, pp.104 - 119

Published online: 31 Mar 2015 *

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