Vertex-dependent filtering of retarded uncertain state-multiplicative noisy systems

The problem of robust H_∞ estimation of stochastic, state-delayed, uncertain, linear, discrete-time systems is solved by applying a vertex dependent Lyapunov function. In this problem, a cost function is defined, which is the expected value of the standard H_∞ performance index with respect to the uncertain parameters. The optimal estimator is obtained by solving a simple set of linear matrix inequalities (LMIs) for either the case where the filter matrices are constant or for the case where these matrices are gain scheduled. The solutions to the corresponding minimum error variance estimation problems are also obtained for the nominal and the uncertain cases, where an additional set of conditions is introduced that guarantees the minimization of the estimation error variance. Two examples are given. The first is a numerical example that demonstrates the advantage of the new design method. The second is an example of a practical nature that is taken from the field of guidance control and estimation.