Robust H-infinity filtering of stationary continuous-time linear systems with stochastic uncertainties

The problem of applying H-infinity-filters on stationary, continuous-time, linear systems with stochastic uncertainties in the state-space signal mode l is addressed. These uncertainties are modeled via white noise processes. The relevant cost function is the expected value of the standard H-infinity performance index with respect to the uncertain parameters. The solution i s obtained via a stochastic bounded real lemma that results in a modified R iccati inequality. This inequality is expressed in the form of a linear mat rix inequality whose solution provides the filter parameters. The method pr oposed is also applied to the case where, in addition to the stochastic unc ertainty, other deterministic parameters of the system are not perfectly kn own and are assumed to lie in a given polytope. The problem of mixed H-2/H- infinity filtering for the above system is also treated. The theory develop ed is demonstrated by a practical example.