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A bst rad;The aim of this paper is to develop an H,-type theory for dicrete time time-varying systems with multiplicative noise. Based on a version of the Bounded Real Lemma corresponding to this class of systems, necessary and sufficient conditions for the existence of a stabilizing determinstic controller ensuring an imposed level of attenuation are derived in terms of the solutions of two linear matrix inequalities (L MI) satisfying a complementary rank condition. Moreover, explicit formulae for such controller are obtained in the case when some additional conditions are assumed. As a particuliw case, we considered the same problem for discrete-time time-varying periodic systems with multiplicative noise, for which it is shown that a periodic yat,tenuating controller may be computed as function of a certain extended LMl's system.

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