Anisotropy-based analysis of linear discrete time varying systems with multiplicative noises

In the 90s of the last century the anisotropy-based control theory was introduced. Its techniques are used in control and filtration problems for linear systems with nonrandom matrices and input random disturbances with unknown statistic characteristics. The concept of anisotropy of random vector as measure of deviation of the vector probabilities distribution law from standard Gauss distribution was introduced in the theory. The paper demonstrates the solutions of anisotropy-based analysis problems for the linear discrete systems with multiplicative noises. The problems of anisotropic norm calculation and formulation of anisotropic norm boundness conditions are considered for such systems on the finite horizon. The anisotropic norm boundness conditions are presented in two forms: the Riccati difference equations and the Riccati inequality. The obtained anisotropy-based analysis results allow to solve control and filtration problems for multiplicative noise systems.