Anisotropy–Based Estimation Design for Linear Discrete Time–Invariant Systems with Measurement Dropouts

This paper considers a time-invariant system with a set of imperfect measurements, the useful component of which may be unavailable at certain times. Virtual objects duplicating the state of the original object are introduced, and an output estimate is constructed for each of them. Using vectorization, an extended model of the system is derived in the form of a linear discrete time-invariant system with multiplicative noises. The external disturbance is chosen from the class of sequences of random vectors with a bounded level of mean anisotropy. For the system describing the estimation error dynamics, conditions for the boundedness of the anisotropic norm are obtained, under which the chosen type of estimator exists. An invertible linearizing change of variables is indicated, which allows reducing the problem of finding the estimator matrices to checking the solvability of a special system of linear matrix inequalities with a convex constraint.