Fixed-order ℌ∞ filtering for discrete-time Markovian jump linear systems with unobservable jump modes

In practical applications, it is often encountered that the jump modes of a Markovian jump linear system may not be fully accessible to the filter, and thus designing a filter which partially or totally independent of the jump modes becomes significant. In this paper, by virtue of a new stability and ℌ∞ performance characterization, a novel necessary and sufficient condition for the existence of mode-independent ℌ∞ filters is established in terms of a set of nonlinear matrix inequalities that possess special properties for computation. Then, two computational approaches are developed to solve the condition. One is based on the solution of a set of linear matrix inequalities (LMIs), and the other is based on the sequential LMI optimization with more computational effort but less conservatism. In addition, a specific property of the feasible solutions enables one to further improve the solvability of these two computational approaches.

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