Model-matching approach to Hinfinity filtering

The H^infinity filtering problem of state estimation for LTI systems is considered. The LTI system is driven at its input and corrupted at its output by processes with known energy bounds (but unknown spectral densities), and state estimates are sought such that the energy of the estimation error is minimised. The H^infinity filtering problem is formulated as a model-matching problem and is solved using a state-space based algebraic approach. A characterisation for a family of H^infinity filters is obtained in the form of a linear fractional transformation. It is shown that the H^infinity filter generalises the Kalman filter and a condition is given under which the H^infinity filter reduces to the Kalman filter. A derivation for minimum-entropy H^infinity filters is given.