Static Output Feedback Stabilization using Invariant Subspaces and Sylvester Equations
DOI:
https://doi.org/10.5540/tema.2009.010.01.0099Resumo
This paper presents systematic computational algorithms for obtaining the output feedback gain matrix in linear systems stabilization problems. Based on the concept of (C,A,B)-invariant subspaces, introduced previously by the first author, that has related the existence of a gain matrix to the solution of coupled Sylvester equations, two algorithms are presented: 1) in the Syrmos-Lewis algorithm, a modification is proposed to provide a more adequate framework to numerical solution, and 2) by using orthogonal transformations, the Alexandridis-Paraskevopoulos algorithm is modified to overcome, in part, the Kimura condition. Numerical examples are provided to illustrate the application of the proposed algorithms.Referências
[1] A.T. Alexandridis, P.N. Paraskevopoulos, A new approach to eigenstructure assignment by output feedback, IEEE Transactions on Automatic Control, 41, No. 7 (1996), 1046–1050.
O. Bachelier, J. Bosche, D. Mehdi, On pole placement via eigenstructure assignment approach, IEEE Transactions on Automatic Control, 51, No. 9 (2006), 1554–1558.
E.B. Castelan, J.C. Hennet, Eigenstructure assignment for state constrained linear continuos time systems, Automatica, 28, No. 3 (1993), 605–611.
E.B. Castelan, J.C. Hennet, E.R.Ll. Villarreal, Quadratic characterization and use of output stabilizable subspaces, in “Proceedings (CD) of the 8th Mediterranean Conference on Control and Automation”, Greece, 2000.
E.B. Castelan, J.C. Hennet, E.R.Ll. Villarreal, Quadratic characterization and use of output stabilizable subspaces, IEEE Transactions on Automatic Control, 48, No. 4 (2003), 654–660.
C.T. Chen, “Linear System Theory ans Design”, Holt, Rinehart and Winston, 1996.
L. Dai, “Singular Control System”, Springer-Verlag, 1989.
J. Dong, G.-H. Yang,Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties, IEEE Transactions on Automatic Control, 52, No. 10 (2007), 1930–1936.
L.R. Fletcher, J. Kautsky, G.K.G. Kolka, N.K. Nichols, Eigenstructure assingment by output feedback in descriptor systems, IEEE Transactions on Automatic Control, 42, No. 4 (1985), 1457–1468.
Y. He, Q.-G. Wang, An improved ILMI method for static output feedback control with application to multivariable PID control, IEEE Transactions on Automatic Control, 51, No. 10 (2006), 1678–1683.
H. Kimura, Pole assignment by gain ouptup feedback, IEEE Transactions on Automatic Control, 20, No. 4 (1975) 509–516.
V.L. Syrmos, F.L. Lewis, Output feedback eigenstructure assignment using two Sylvester equations, IEEE Transactions on Automatic Control, 38, No. 3(1993), 495–499.
V.L. Syrmos, F.L. Lewis, Transmission zero assignment using descriptions, IEEE Transactions on Automatic Control, 38, No. 7 (1993), 1115–1120.
V.L. Syrmos, F.L. Lewis, Bilinear formulation for the output feedback problem in linear system, IEEE Transactions on Automatic Control, 39, No. 2 (1994), 410–414.
V.L. Syrmos, C.T. Abdallah, P. Dorato, K. Grigoriadis, Static output feedback - a survey, Automatica, 33, No. 2 (1997), 125–137.
E.R.Ll. Villarreal, J.D. Lima, Approach for stabilization by output feedback, invariant subspaces and Sylvester equations, in “Anais CNMAC 2008”, Belém, PA, Brasil.
W.M. Wonahm, “Linear Multivariable Control, a Geometric Approach”, Springer-Verlag, 1979.
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