\(H_ \infty\) estimation for uncertain systems.

*(English)*Zbl 0765.93032Summary: 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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\textit{M. Fu} et al., Int. J. Robust Nonlinear Control 2, No. 2, 87--105 (1992; Zbl 0765.93032)

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