On the Anisotropy-Based Bounded Real Lemma Formulation for the Systems with Disturbance-Term Multiplicative Noise**The paper is supported by the Russian Foundation for Basic Research (grants 14-08-00069, 15-07-05489 and 16-38-00216)

This paper is an attempt to present the methodologically correct approach of the anisotropy-based theory for discrete-time systems with multiplicative noise. A formulation of sufficient conditions of boundedness of the anisotropic norm is the main goal of this paper. As it is shown, this problem can be reduced to the convex optimization problem. A simple numerical example to illustrate the solution procedure is given.