Title: Linear hybrid systems with time-varying delays: H_∞ stabilisation schemes

Authors: Magdi S. Mahmoud

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

Abstract: In this paper, we provide new stabilisation schemes for a class of linear Hybrid Time-Delay (HTD) systems under arbitrary switching. These schemes are delay-independent and delay-dependent H_∞ stabilisation based on Proportional-Integral-Derivative (PID) feedback strategy. By adopting a selective Lyapunov-Krasovskii Functional (LKF), new criteria are constructed in a systematic way in terms of feasibility-testing of Linear Matrix Inequalities (LMIs). When the time-delay is a continuous bounded function, we derive the solution for nominal and polytopic models as well identifying several existing results as special cases. In case the time-delay is a differentiable time-varying function satisfying some bounding relations, we establish new parametrised LMI characterisations for PID feedback stabilisation. Numerical examples are provided to illustrate the theoretical developments.

Keywords: hybrid time-delay systems; PID feedback; proportional-integral-derivative feedback; feedback stabilisation; LMIs; linear matrix inequalities; arbitrary switching; time-varying delays; feedback control; PID control.

DOI: 10.1504/IJSCC.2008.021119

International Journal of Systems, Control and Communications, 2008 Vol.1 No.2, pp.147 - 169

Published online: 04 Nov 2008 *

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