Fixed-order robust H∞ filter design for Markovian jump systems with uncertain switching probabilities

This paper discusses the fixed-order robust H_∞ filtering problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration are assumed to be norm-bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix, respectively. First, a criterion based on linear matrix inequalities is provided for testing the H_∞ filtering level of a filter over all the admissible uncertainties. Then, a sufficient condition for the existence of the fixed-order robust H_∞ filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints. To determine the filter, a globally convergent algorithm involving convex optimization is suggested. Finally, a numerical example is used to illustrate that the developed theory is more effective than the existing results.