Robust H∞ filtering with parametric uncertainty and deterministic input signal

Many dynamical signal processes involve not only process and measurement noises but also parameter uncertainty and known input signals. When an L₂ and H_∞ filter designed based on a nominal model of the process is 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. The authors develop a finite horizon robust H_∞ filtering method which provides a guaranteed H_∞ bound for the estimation error in the presence of both parameter uncertainty and known input signal. This method is developed by using a game-theoretical approach, and the results generalize those for the case either without parameter uncertainty or without a known input signal