Petersen, Ian R. A notion of possible controllability for uncertain linear systems with structured uncertainty. (English) Zbl 1154.93319 Automatica 45, No. 1, 134-141 (2009). Summary: This paper introduces a notion of possible controllability for a class of uncertain linear systems with structured uncertainty described by averaged integral quadratic constraints. This notion relates to the question of when a state is controllable for some possible value of the uncertainty. The notion of possible controllability is motivated by a desire to extend the theory of minimal realization for linear time invariant systems to the case of uncertain systems with structured uncertainty. Cited in 5 Documents MSC: 93B05 Controllability 93C05 Linear systems in control theory Keywords:uncertain systems; controllability; uncertainty; integral quadratic constraints; controllability Gramian PDFBibTeX XMLCite \textit{I. R. Petersen}, Automatica 45, No. 1, 134--141 (2009; Zbl 1154.93319) Full Text: DOI References: [1] Beck, C. L.; Doyle, J. C., A necessary and sufficient minimality condition for uncertain systems, IEEE Transactions on Automatic Control, 44, 10, 1802-1813 (1999) · Zbl 0956.93012 [2] Chung, D.; Park, C. G.; Lee, J. G., Robustness of controllability and observability of continuous linear time-varying systems with parameter perturbations, IEEE Transactions on Automatic Control, 44, 1919-1923 (1999) · Zbl 0956.93043 [3] Clements, D. J.; Anderson, B. D.O., Singular optimal control: The linear-quadratic problem (1978), Springer Verlag: Springer Verlag Berlin, Germany · Zbl 0348.49003 [4] Kailath, T., Linear systems (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0458.93025 [5] Megretsky, A.; Treil, S., Power distribution inequalities in optimization and robustness of uncertain systems, Journal of Mathematical Systems, Estimation and Control, 3, 3, 301-319 (1993) · Zbl 0781.93079 [6] Petersen, I., Robust unobservability for uncertain linear systems with structured uncertainty, IEEE Transactions on Automatic Control, 52, 8, 1461-1469 (2007) · Zbl 1366.93081 [7] Petersen, I. R.; Ugrinovskii, V.; Savkin, A. V., Robust control design using \(H^\infty\) methods (2000), Springer-Verlag: Springer-Verlag London · Zbl 0963.93003 [8] Poolla, K.; Tikku, A., Robust performance against time-varying structured perturbations, IEEE Transactions on Automatic Control, 40, 9, 1589-1602 (1995) · Zbl 0831.93019 [9] Sastry, S. S.; Desoer, C. A., The robustness of controllability and observability of linear time-varying systems, IEEE Transactions on Automatic Control, 27, 933-939 (1982) · Zbl 0486.93013 [10] Savkin, A. V.; Petersen, I. R., Uncertainty averaging approach to output feedback optimal guaranteed cost control of uncertain systems, Journal of Optimization Theory and Applications, 88, 2, 321-337 (1996) · Zbl 0853.93065 [11] Scherpen, J.; Gray, W., Minimality and local state decompositions of a nonlinear state space realization using energy functions, IEEE Transactions on Automatic Control, 45, 11, 2079-2086 (2000) · Zbl 0989.93017 [12] Ugrinovskii, V. A., Robust controllability of linear stochastic uncertain systems, Automatica, 41, 807-813 (2005) · Zbl 1098.93006 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.