H-infinity control and filtering of discrete-time stochastic systems with multiplicative noise

Linear discrete-time systems with stochastic uncertainties in their state-s pace matrices are considered. The problems of finite-horizon filtering and output-feedback control are solved, taking into account possible cross-corr elations between the uncertain parameters. In both problems, a cost functio n is defined which is the expected value of the relevant standard H-infinit y performance index with respect to the uncertain parameters. A solution to the filtering problem is obtained first by applying the adjoint system and deriving a bounded real lemma for this system. This solution guarantees a prescribed estimation level of accuracy while minimizing an upper bound on the covariance of the estimation error. The solution of the filtering probl em is also extended to the infinite-horizon case. The results of the filter ing problem are used to solve the corresponding output-feedback problem. A filtering example is given where a comparison is made with the results obta ined using bounded uncertainty design techniques. (C) 2001 Elsevier Science Ltd. All rights reserved.