Robust H∞ Filtering for Continuous Time Varying Uncertain Systems with Deterministic Input Signals

Many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals. When L2 or H∞n filters that were designed based on a “nominal" model of the system are applied, the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal, and the latter may be very appreciable. In this paper, we introduce a finite-horizon robust H∞ filtering method that provides a guaranteed H∞ bound for the estimation error in the presence of both parameter uncertainty and a known input signal. This method is developed by using a game-theoretic approach, and the results generalize those obtained for cases without parameter uncertainty or without a known input signal. It is also demonstrated, via an example, that the proposed method provides significantly improved signal estimates.