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Feedback Stabilization of Singularly Perturbed Systems Under Information Constraints
Author(s) -
Wang Yanyan,
Liu Wei,
Xu Jianzhong
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1267
Subject(s) - control theory (sociology) , exponential stability , upper and lower bounds , singular perturbation , perturbation (astronomy) , full state feedback , controller (irrigation) , mathematics , simple (philosophy) , stability (learning theory) , class (philosophy) , state (computer science) , channel (broadcasting) , transmission (telecommunications) , control system , computer science , control (management) , engineering , nonlinear system , algorithm , telecommunications , mathematical analysis , philosophy , physics , electrical engineering , epistemology , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
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.