Linear hybrid systems with time-varying delays: H_∞ stabilisation schemes
by Magdi S. Mahmoud
International Journal of Systems, Control and Communications (IJSCC), Vol. 1, No. 2, 2008

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.

Online publication date: Tue, 04-Nov-2008

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