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Feedback stabilization of singularly perturbed systems under information constraints. (English) Zbl 1347.93207

Summary: The quantized feedback control for a class of singularly perturbed systems is addressed, in which the controlled system and the controller are connected via a limited capacity communication channel. First, a proper coder-decoder pair is presented such that the transmission error decays to zero exponentially under information constraints. Then, a control law in terms of linear matrix inequalities is constructed to render the resulting closed-loop system input-to-state stable with regard to the transmission error. Thus, the asymptotic stability of the closed-loop system is guaranteed. It is shown that the proposed method is simple and easy to operate. Moreover, an upper bound of the small perturbation parameter for the stability of systems can be explicitly estimated with a workable computational way. Finally, two examples are presented to show the effectiveness of the proposed method.

MSC:

93D15 Stabilization of systems by feedback
93C70 Time-scale analysis and singular perturbations in control/observation systems
93D25 Input-output approaches in control theory
93C15 Control/observation systems governed by ordinary differential equations
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