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

Xi-Kui Liu, Ji-Jing Zhuang, and Yan Li*
International Journal of Control, Automation, and Systems, vol. 19, no. 7, pp.2500-2510, 2021

Abstract : 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.

Keyword : H∞ filtering, Markov jump, stochastic system, uncertain transition probabilities.

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