“Maximal imaginery eigenvalues in optimal systems”
Authors: David Di Ruscio,Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1991, Vol 12, No 3, pp. 149-158.
Keywords: Linear optimal control, pole placement, eigenvalues, multivariable control systems, control system design
Abstract: In this note we present equations that uniquely determine the maximum possible imaginary value of the closed loop eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen, provided a real symmetric solution of the algebraic Riccati equation exists. In addition, the corresponding state weight matrix and the solution to the algebraic Riccati equation are derived for a class of linear systems. A fundamental lemma for the existence of a real symmetric solution to the algebraic Riccati equation is derived for this class of linear systems.
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DOI: 10.4173/mic.1991.3.5DOI forward links to this article:
| [1] D. Di Ruscio (1991), doi:10.1109/CDC.1991.261580 |
| [2] D. Di Ruscio (1992), doi:10.1109/CDC.1992.371469 |
[1] DI RUSCIO, D. BALCHEN, J.G. (1990). A Schur method for designing LQ-optimal systems with prescribed eigenvalues, Modeling, Identification and Control, 11, 55-72 doi:10.4173/mic.1990.1.5
[2] KUCERA, V. (1989). Algebraic Riccati equation: Symmetric and definite solutions, Workshop on The Riccati equation in control systems, and signals. Como, Italy 1989. With the participation of IEEE-Control Systems Society. Printed by Pitagora Editrice Bologna, Via del Legatore 3, Bologna.
[3] LANCASTER, P. RODMAN, L. (1980). Existence and uniqueness theorems for the algebraic Riccati equation, Int. J. Control, 32, 285-309 doi:10.1080/00207178008922858
[4] LAUB, A.J. (1979). A Schur Method for Solving Algebraic Riccati Equations, IEEE Trans. on Automatic Control, 24, 913-921 doi:10.1109/TAC.1979.1102178
[5] WILLEMS, J.C. (1971). Least Squares Stationary Optimal Control and the Algebraic Riccati Equation, IEEE Trans. on Automatic Control, 16, 621-634 doi:10.1109/TAC.1971.1099831
BibTeX:
@article{MIC-1991-3-5,
title={{Maximal imaginery eigenvalues in optimal systems}},
author={Di Ruscio, David},
journal={Modeling, Identification and Control},
volume={12},
number={3},
pages={149--158},
year={1991},
doi={10.4173/mic.1991.3.5},
publisher={Norwegian Society of Automatic Control}
};