Mehdi, Driss; Al Hamid, Mohammed; Perrin, François Robustness and optimality of linear quadratic controller for uncertain systems. (English) Zbl 0855.49024 Automatica 32, No. 7, 1081-1083 (1996). Summary: In this paper, we present a linear quadratic design for uncertain systems in state space representation. The parameter uncertainty is structured and value bounded. We show also that with a controller of this type, the optimality of the LQ regulator is preserved in the presence of uncertainty. Cited in 1 ReviewCited in 3 Documents MSC: 49N10 Linear-quadratic optimal control problems 93B35 Sensitivity (robustness) Keywords:linear quadratic regulators; optimality; robust stability; robustness; uncertain linear systems; LQ regulator PDF BibTeX XML Cite \textit{D. Mehdi} et al., Automatica 32, No. 7, 1081--1083 (1996; Zbl 0855.49024) Full Text: DOI References: [1] Anderson, B.D.O.; Moore, J.B., () [2] Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system, J. optimization theory and applications, 46, 399-408, (1985) · Zbl 0549.93045 [3] Chang, S.S.L.; Peng, T.K.C., Adaptive guaranteed cost control systems with uncertain parameters, IEEE trans. automat. control, 17, 474-483, (1972) · Zbl 0259.93018 [4] Dorato, P.; Abdellah, C.; Cerone, V., () [5] Douglas, J.; Athans, M., Robust linear quadratic designs with real parameter uncertainty, IEEE trans. automat. control, AC-39, 107-111, (1994) · Zbl 0796.93025 [6] Gu, K.; Zohdy, M.A.; Loh, N.K., Necessary and sufficient condition of quadratic stability of uncertain linear systems, IEEE trans. automat. control, AC-35, 601-604, (1990) · Zbl 0705.93064 [7] Kosmidou, O.I., Robust stability and performance of systems with structured and bounded uncertainties: an extension of the guaranteed cost control approach, Int. J. control, 52, 627-640, (1990) · Zbl 0711.93044 [8] Molinari, B.P., The stable regulator problem and its inverse, IEEE trans. automat. control, AC-18, 454-459, (1973) · Zbl 0263.49029 [9] Petersen, I.; Hollot, C.V., A Riccati equation approach in the stabilization of uncertain linear systems, Automatica, 22, 397-411, (1986) · Zbl 0602.93055 [10] Petersen, I.R., A stabilization algorithm for a class of uncertain linear systems, Syst. & control lett., 8, 351-357, (1987) · Zbl 0618.93056 [11] Schmitendorf, W.E., Design methodology for robust stabilizing controllers, J. guidance, 10, 250-254, (1987) · Zbl 0631.93060 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.