×

Asymptotic expansions for game-theoretic Riccati equations and stabilization with disturbance attenuation for singularly perturbed systems. (English) Zbl 0784.93040

Summary: If the systems to be controlled are singularly perturbed, then the Riccati equations which appear in \(H_ \infty\) problems are difficult to solve due to the presence of the small parameter. The present paper describes and validates asymptotic expansions, showing how they may be used in \(H_ \infty\) control. Furthermore, we construct a composite controller based on the solution of slow and fast problems, which guarantees a desired achievable performance level for the full-order plant as \(\varepsilon\) approaches zero.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
93C73 Perturbations in control/observation systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Doyle, J.C.; Glover, K.; Khargonekar, P.P.; Francis, B.A., State-space solutions to standard H2 and H∞ control problems, IEEE trans. automat. control, 34, 8, (1989)
[2] Drǎgan, V.; Halanay, A., Uniform asymptotic expansions for the fundamental matrix of singularly perturbed linear systems and applications, () · Zbl 0509.34059
[3] Saksena, V.R.; O’Reilly, J.; Kokotovic, P.V., Singular perturbations and time-scale methods in control theory: survey 1976-1983, Automatica, 20, 273-293, (1984) · Zbl 0532.93002
[4] Pan, Zigang; Başar, Tamer, H∞ optimal control for singularly perturbed systems — part I. perfect state measurements, (), Automatica, to appear · Zbl 0782.49015
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.