In this paper, we provide new stabilization schemes for a class of linear hybrid time-delay systems under arbitrary switching. These schemes are delay-independent and delay-dependent stabilization based on proportional-plus-derivative (PPD) feedback strategy. By adopting a selective Lyapunov–Krasovskii functional, 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 and identify several existing results as special cases. In case the time delay is a differentiable time-varying function satisfying some bounding relations, we establish a new parametrized LMI characterization for PPD feedback stabilization. The theoretical developments are illustrated on examples of combustion in rocket motor chambers, river pollution control, and resilience analysis, and the ensuing results are compared with the conventional feedback stabilization.
New Stabilization Schemes for Linear Hybrid Systems With Time-Varying Delays
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Mahmoud, M. S., and Elferik, S. A. (August 19, 2010). "New Stabilization Schemes for Linear Hybrid Systems With Time-Varying Delays." ASME. J. Dyn. Sys., Meas., Control. September 2010; 132(5): 051007. https://doi.org/10.1115/1.4002102
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