Reduced order H-infinity deconvolution filter design and applications

The object of this thesis is to develop a class of H∞ deconvolution filters. The methods used are differential game theory and the Bounded Real Lemma. Game theory has been useful in designing H∞ filters because H∞ filtering is a minimax problem. The H∞ filter minimizes a payoff function while the external disturbance maximizes it. The Bounded Real Lemma method is known as a Riccati equation technique. These two approaches are applicable for both continuous and discrete time-varying or time-invariant linear systems.; A game theoretic approach of designing a robust H∞ deconvolution filter for systems with parameter uncertainty is presented in the first part of the thesis. The resulting filter design can be accomplished by solving two Riccati matrix equations.; The Bounded Real Lemma approach of designing reduced-order H ∞ deconvolution filters is presented in the second part of the thesis. It is shown that the order of filter can be lower than n − p, where n is the order of the system and p is the order of the measured output. The derived Riccati matrix equation for reduced order deconvolution filtering is different from the conventional one. The new reduced order filter design is applied to two examples, namely, image restoration and communication channel equalization.; In the last part of the thesis, an application of H∞ state estimators to the tracking of power system harmonics is presented. For comparison, a Kalman filter is applied to the same application.