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IMA Journal of Mathematical Control and Information 2004 21(2):143-158; doi:10.1093/imamci/21.2.143
© 2004 by Institute of Mathematics and its Applications
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Reduced-order filtering with energy-to-peak performance for discrete-time Markovian jumping systems

Huaping Liu1, Fuchun Sun1 and Zengqi Sun1

1 Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, People's Republic of China and State Key Laboratory of Intelligent Technology and Systems, Beijing, 100084, People's Republic of China

In this paper, the l2–l{infty} (energy-to-peak) performance of the discrete-time Markovian jump linear system is investigated. The jump parameters are modelled by a discrete-time Markov process. Furthermore, we study the l2–l{infty} reduced-order filtering problem for the Markovian jump linear system. A reduced-order filter with the same randomly jumping parameters is proposed which can make the error systems with Markovian jump parameters stochastically stable with a prescribed l2–l{infty}performance. Sufficient conditions in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint are derived for the existence of a solution to the reduced-order filtering problems. A numerical example is given to illustrate the design procedures.

Keywords: energy-to-peak performance; jumping parameters; linear matrix inequalities; reduced-order filtering.

Received 6 June 2003.


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