H∞ estimation for uncertain systems

Abstract This paper deals with the problem of H ∞ estimation for linear systems with a certain type of time‐varying norm‐bounded parameter uncertainty in both the state and output matrices. We address the problem of designing an asymptotically stable estimator that guarantees a prescribed level of H ∞ noise attenuation for all admissible parameter uncertainties. Both an interpolation theory approach and a Riccati equation approach are proposed to solve the estimation problem, with each method having its own advantages. The first approach seems more numerically attractive whilst the second one provides a simple structure for the estimator with its solution given in terms of two algebraic Riccati equations and a parameterization of a class of suitable H ∞ estimators. The Riccati equation approach also pinpoints the ‘worst‐case’ uncertainty.