Synthesis of stable linear Pugachev filters and extrapolators for stochastic systems with wide band multiplicative noises

The article is dedicated to the analytical synthesis of continuous and discrete uniquely asymptotically stable conditionally optimal linear Pugachev filters and extrapolators (LPF and LPE) for stochastic systems (StS) with wide band multiplicative Gaussian noises. It is supposed that observation is part of the state and observation equations. The theorems serving as the basis for the algorithms of synthesis of continuous uniquely asymptotical stable LPF and LPE are proven. Continuous LPF and LPE for StS with wide band Gaussian autocorrelated noises are presented. Discrete LPF and LPE for continuous and discrete StS with wide band multiplicative Gaussian noises are considered. An illustrative example is given. Some generalizations are considered.