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Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises
Author(s) -
Sheng Li,
Niu Yichun,
Gao Ming,
Zhou Donghua
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.5033
Subject(s) - polynomial , nonlinear system , matrix polynomial , mathematics , control theory (sociology) , bounded function , state (computer science) , taylor series , filter (signal processing) , computer science , mathematical analysis , algorithm , control (management) , physics , quantum mechanics , artificial intelligence , computer vision
Summary This article is concerned with the polynomial filtering problem for a class of nonlinear stochastic systems governed by the Itô differential equation. The system under investigation involves polynomial nonlinearities, unknown‐but‐bounded disturbances, and state‐ and disturbance‐dependent noises (( x , d )‐dependent noises for short). By expanding the polynomial nonlinear functions in Taylor series around the state estimate, a new polynomial filter design method is developed with hope to reduce the conservatism of the existing results. In virtue of stochastic analysis and inequality technique, sufficient conditions in terms of parameter‐dependent linear matrix inequalities (PDLMIs) are derived to guarantee that the estimation error system is input‐to‐state stable in probability. Moreover, the desired polynomial matrix can be obtained by solving the PDLMIs via the sum‐of‐squares approach. The effectiveness and applicability of the proposed method are illustrated by two numerical examples with one concerning the permanent magnet synchronous motor.