H∞ State estimation for stochastic state multiplicative systems

The problem of $H_{\infty}$ state estimation is considered for uncertain polytopic linear discrete-time stochastic state-multiplicative systems. We first bring a unique version of the BRL for the latter systems which allows for vertex-dependent solution in the uncertain case. Following the BRL derivation, we solve the estimation problem for nominal systems which serves as a basis for extracting the filter parameters in the uncertain case. In both cases: the nominal and the uncertain cases, the filter parameters are extracted by a solving an LMI condition in the former case or a set of LMIs in the latter case, both of which depend on a minimal set of tuning parameters, thus greatly reduce the over-design. The theory presented is demonstrated by a numerical example.