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Attractive ellipsoid design for robust sliding‐mode observation error in stochastic nonlinear discrete‐time systems
Author(s) -
Velázquez David,
Poznyak Alex
Publication year - 2020
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.5270
Subject(s) - ellipsoid , control theory (sociology) , lipschitz continuity , nonlinear system , mathematics , residual , linear matrix inequality , discrete time and continuous time , observer (physics) , convex optimization , robust control , mathematical optimization , computer science , regular polygon , algorithm , mathematical analysis , control (management) , statistics , physics , quantum mechanics , artificial intelligence , geometry , astronomy
Summary In this paper the observation process of stochastic discrete‐time nonlinear system is analyzed. The system to be observed is assumed to be uncertain, but fulfilling the global "quasi‐Lipschitz" condition and is subjected to stochastic input and output disturbances of a white noise type. The combination of a traditional Luenberger residual term with a discontinuous one is considered. The designing of the best observer gain matrices is realized by using the Robust Attractive Ellipsoid Method for the analysis of the averaged observation error. The construction of this attractive ellipsoid is based on the numerical solution of some matrix optimization problem under specific constraints of Bilinear and Linear Matrix Inequalities (BMI's and LMI's) type applied to improve the attractiveness zone estimation. Two numerical xamples illustrate the effectiveness of the suggested approach.