Design of probabilistic $ l_2-l_\infty $ filter for uncertain Markov jump systems with partial information of the transition probabilities

Abstract

<p style='text-indent:20px;'>In this paper, the problem of <inline-formula><tex-math id="M2">\begin{document}$ l_2-l_\infty $\end{document}</tex-math></inline-formula> probabilistic filtering for uncertain Markov jump systems with partial information of the transition probabilities is studied, where the uncertainties are caused by randomly changing interior parameters. Combining the original system and the filtering system, an augmented error system is proposed. Some concepts of probability theory are introduced to handle the uncertainties. Due to the complicated structure of real practical systems, only partial information on the transition probabilities are available. In this paper, by using Lyapunov functional method and probability theory, linear matrix inequalities (LMIs) type of sufficient conditions are derived. Based on these sufficient conditions, a probability filter is constructed such that the augmented error system with partial information of the transition probabilities is stochastically stable with a given confidence level and satisfying an <inline-formula><tex-math id="M3">\begin{document}$ l_2-l_\infty $\end{document}</tex-math></inline-formula> performance index. Furthermore, the gain matrices of the filter are obtained through the introduction of slack matrices. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.</p>