INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2003; 13:1299–1316 (DOI: 10.1002/rnc.843) H 1 filtering for discrete-time linear systems with Markovian jumping parameters y Carlos E. de Souza z and Marcelo D. Fragoso n,} Department of Systems and Control, Laborat ! orio Nacional de Computac ¸ * ao Cient ! ıfica – LNCC/MCT, Av. Getulio Vargas 333, 25651-070-Petr ! opolis, RJ, Brazil SUMMARY This paper investigates the problem of H 1 filtering for discrete-time linear systems with Markovian jumping parameters. It is assumed that the jumping parameter is available. This paper develops necessary and sufficient conditions for designing a discrete-time Markovian jump linear filter which ensures a prescribed bound on the ‘ 2 -induced gain from the noise signals to the estimation error. The proposed filter design is given in terms of linear matrix inequalities. Copyright # 2003 John Wiley & Sons, Ltd. KEY WORDS: H 1 filtering; Markovian jump linear systems; discrete-time systems; state estimation; linear matrix inequalities 1. INTRODUCTION The H 1 approach has crop out as a very powerful tool within the context of filtering theory in recent years. This is particularly true if we are dealing with the very common situation in which we do not know precisely the statistics of the additive noise actuating in the system. The H 1 approach hinges on the use of a nowadays very popular measure of performance, the H 1 - norm, or equivalently, the ‘ 2 -induced gain (in the discrete-time case). In this context, the filtering problem is known in the literature as the H 1 filtering problem, and has attracted considerable attention (see, e.g. References [1–7] and the references therein). Roughly speaking, in the H 1 filtering approach the noise sources one considers are arbitrary signals with bounded energy, or bounded average power, and the estimator is designed to guarantee that the ‘ 2 -induced gain, from the noise signals to the estimation error, be less than a prescribed bound. The potential of H 1 filtering lies far beyond its insensitivity to the noise statistics. It has been recognized in Received 9 May 2002 Published online 6 October 2003 Accepted 27 February 2003 Copyright # 2003 John Wiley & Sons, Ltd. y A preliminary version of this paper was presented at the 36th IEEE Conference on Decision and Control, San Diego, CA, 1997. z E-mail: csouza@lncc.br n Correspondence to: Prof. M. D. Fragoso, National Laboratory for Scientific Computing, LNCC/MCT, Department of Systems and Control, Av. Getulio Vargas 333, Quitandinha, 25651-070-Petro´polis, Rio de Janeiro, Brazil. } E-mail: frag@lncc.br Contract/grant sponsor: Conselho Nacional de Desenvolvimento Cient ! ıfico e Tecnol ! ogico}CNPq; contract/grant number: PRONEX 0331.00/00, 46.8652/00-0/APQ, 46.5532/00-4/APQ, IM-AGIMB, 30.1653/96-8/PQ, 52.0169/97-2/PQ