zbMATH — the first resource for mathematics

\(H_ \infty\) 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.

93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
Full Text: DOI
[1] and , Optimal Filtering, Prentice Hall, Englewood Cliffs, NJ, 1979.
[2] Bernstein, System & Control Lett. 12 pp 9– (1989)
[3] and , On the properties of indefinite algebraic Riccati equations, Tech. Report EE8952, Dept. Elec. & Comp. Eng., University of Newcastle, NSW, Australia, August 1989.
[4] Doyle, IEEE Trans. Automat. Control 39 pp 831– (1989)
[5] A Course in H Control Theory, Springer-Verlag, New York, 1987.
[6] Exact, optimal and partial loop transfer recovery, Proc. 29th IEEE Conf. on Decision and Control, Honolulu, Hawaii, December 1990, pp. 1841–1846.
[7] Fu, Systems & Control Letters 17 pp 29– (1991)
[8] H design of optimal linear filters, in Linear Circuits, Systems and Signal Processing: Theory and Application, and (Eds), North-Holland, Amsterdam, 1988, pp. 533–540.
[9] Grimble, IEEE Trans. Acoust., Speech and Signal Processing 38 pp 1092– (1990)
[10] , and , H robust linear estimator, Proc. IFAC Symp. Adaptive Syst. in Control and Signal Processing, Glasgow, April 1989, pp. 159–164.
[11] Khargonekar, IEEE Trans. Automat. Control 35 pp 356– (1990)
[12] Khargonekar, SIAM J. Contr. and Optimiz. 29 pp 1373– (1991)
[13] Limebeer, Linear Algebra and its Applications 98 pp 347– (1988)
[14] Nagpal, IEEE Trans. Automat. Control 36 pp 152– (1991)
[15] Petersen, IEEE Trans. Automat. Control 32 pp 427– (1987)
[16] Safonov, Int. J. Control 50 pp 2467– (1989)
[17] Shaked, IEEE Trans. Automat. Control 35 pp 554– (1990)
[18] and , Robust H, control for linear systems with norm-bounded time-varying uncertainty, IEEE Trans. Automat. Control, 1992, to appear.
[19] and , H, state estimation for linear periodic systems, Proc. 29th IEEE Conf. on Decision and Control, Honolulu, Hawaii, December 1990, pp. 3188–3193.
[20] , and , H control and quadratic stabilization of systems with parameter uncertainty via output feedback, IEEE Trans. Automat. Control, 1992, to appear. · Zbl 0764.93067
[21] and , Game theory approach to optimal linear estimation in the minimum Hx-norm sense, Proc. 28th IEEE Conf. Decision and Control, Tampa, FL, December 1989, pp. 415–420.
[22] and , Optimal control and estimation of uncertain linear time-varying systems, preprint.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.