Robust $L_{\infty }$ -Induced 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 induced L_∞ state-feedback control and filtering are solved, for the stationary case. In both problems, the cost function is defined to be the expected value of the standard induced L_∞ performance index with respect to the uncertain parameters. An example that demonstrates the applicability of the theory is given.