Robust L∞-induced optimal filtering and control of stochastic systems with state-multiplicative noise

Linear, continuous-time systems with stochastic uncertainties in their state-space model are considered. The problems of L
_∞
state-feedback control and filtering are solved for the stationary case. In both problems, a cost function which is the expected value of the standard induced L
_∞
norm performance index with respect to the uncertain parameters is defined. An example which demonstrates the applicability of the theory is given.