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\(H_ \infty\) estimation for uncertain systems. (English) Zbl 0765.93032
Summary: This paper deals with the problem of \(H_ \infty\) 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 \(H_ \infty\) 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 \(H_ \infty\) estimators. The Riccati equation approach also pinpoints the ‘worst-case’ uncertainty.

MSC:
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
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