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Invariant set analysis for SISO discrete‐time polynomial systems with dynamic quantizers
Author(s) -
Ichihara Hiroyuki,
Sawada Kenji,
Tarbouriech Sophie
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4326
Subject(s) - quantization (signal processing) , bounded function , mathematics , control theory (sociology) , invariant (physics) , discrete time and continuous time , polynomial , regular polygon , lti system theory , computer science , algorithm , linear system , artificial intelligence , mathematical analysis , control (management) , geometry , statistics , mathematical physics
Summary This paper deals with the stability analysis problem of discrete‐time polynomial systems subject to input quantization. The quantizer under consideration is supposed to be dynamic. Indeed, considering the quantization error as bounded disturbances, the regional input‐to‐state stability is studied. The approach developed consists in characterizing two nested invariant sets where the outer one is a region of attraction and the inner one is the robust invariant set with respect to the quantization error. By defining a performance index between the quantized system and the quantizer‐free system, a quasi‐convex problem is formulated to minimize an upper bound on such a performance index.