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Wirtinger’s inequality and Lyapunov-based sampled-data stabilization. (English) Zbl 1244.93094

Summary: Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems E. Fridman [”A refined input delay approach to sampled-data control, Automatica 46, No. 2, 421-427 (2010; Zbl 1205.93099)] and P. Naghshtabrizi, J. Hespanha, A. R. Teel [”Exponential stability of impulsive systems with application to uncertain sampled-data systems, Syst. Control Lett. 57, No. 5, 378-385 (2008; Zbl 1140.93036)]. In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger’s inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.

MSC:

93C57 Sampled-data control/observation systems
93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
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