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

Authors:
Magdi S. Mahmoud
Affiliations:
Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran 31261, Saudi Arabia
Venue:
International Journal of Systems, Control and Communications
Year:
2008

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Abstract

In this paper, we provide new stabilisation schemes for a classof linear Hybrid Time-Delay (HTD) systems under arbitraryswitching. These schemes are delay-independent and delay-dependentH∞ stabilisation based onProportional-Integral-Derivative (PID) feedback strategy. Byadopting a selective Lyapunov-Krasovskii Functional (LKF), newcriteria are constructed in a systematic way in terms offeasibility-testing of Linear Matrix Inequalities (LMIs). When thetime-delay is a continuous bounded function, we derive the solutionfor nominal and polytopic models as well identifying severalexisting results as special cases. In case the time-delay is adifferentiable time-varying function satisfying some boundingrelations, we establish new parametrised LMI characterisations forPID feedback stabilisation. Numerical examples are provided toillustrate the theoretical developments.