H∞ Filtering for Markovian Jump Linear Systems with Uncertain Transition Probabilities

• Published in: International journal of control, automation, and systems Vol. 19; no. 7; pp. 2500 - 2510
• Main Authors: Liu, Xi-Kui, Zhuang, Ji-Jing, Li, Yan
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.07.2021; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Control; Control Theory and Applications; Coupling; Decoupling method; Discrete time systems; Engineering; Filtration; H-infinity control; Linear matrix inequalities; Linear systems; Mathematical analysis; Mechatronics; Robotics; Stochastic systems; Transition probabilities; 제어계측공학; stochastic system; Markov jump; filtering; uncertain transition probabilities
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-020-0129-y

This paper studies the H ∞ filtering problem of stochastic linear systems subject to Markovian jump and multiplicative noise. The transition probabilities are considered to be uncertain. A unified form of filters is constructed for both continuous-time and discrete-time stochastic systems. With the new decoupling technique for the coupling terms between Lyapunov matrices and filtering parameters, sufficient conditions of stochastic stability and H ∞ performance of filtering error system are derived. Based on these conditions, the filter is designed with less coupling matrices and the filter gain matrices are obtained by calculating a set of linear matrix inequalities. Finally, three examples are presented to test the effectiveness of the obtained method.