×

The row-by-row decoupling via state feedback: A polynomial approach. (English) Zbl 0790.93075

Summary: Necessary and sufficient conditions for the row-by-row and integrator decoupling of a linear system \(\dot x= Ax+ Bu\), \(y= Cx\) via nonregular static state feedback are established. A procedure is outlined to calculate one such gain.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
93B52 Feedback control
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Commault, C.; Descusse, J.; Dion, J. M.; Lafay, J. F.; Malabre, M., New decoupling invariants: the essential orders, Int. J. Control, 44, 689-700 (1986) · Zbl 0611.93012
[2] Descusse, J.; Lafay, J. F.; Malabre, M., Solution to Morgan’s problem, IEEE Trans. Aut. Control, AC-33, 732-739 (1988) · Zbl 0656.93018
[3] Dion, J. M.; Commault, C., The minimal delay decoupling problem: feedback implementation with stability, SIAM. J. Control Optimiz., 26, 66-82 (1988) · Zbl 0646.93049
[4] Falb, P. L.; Wolovich, W. A., Decoupling in the design and synthesis of multivariable control systems, IEEE Trans. Aut. Control, AC-12, 651-669 (1967)
[5] Herrera, A. N.; Lafay, J. F.; Zagalak, P., The extended interactor in the study of nonregular control problems, (Proc. 30th IEEE Conf. On Decision and Control. Proc. 30th IEEE Conf. On Decision and Control, Brighton, U.K. (1991)), 373-377
[6] Herrera, A. N.; Lafay, J. F., New results about the Morgan’s problem, IEEE Trans. Aut. Control (1992), submitted · Zbl 0792.93083
[7] Kailath, T., (Linear Systems (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ) · Zbl 0458.93025
[8] Kučera, V., (Discrete Linear Control: The Polynomial Equation Approach (1979), Wiley: Wiley Chichester)
[9] Kučera, V.; Zagalak, P., Constant solutions of polynomial equations, Int. J. Control, 53, 495-502 (1991) · Zbl 0731.15009
[10] Loisequ, J. J., Sur la modification de la structure a l’infini par retour d’etat statique, SIAM J. Control Optimiz., 26, 251-273 (1988)
[11] Morgan, B. S., The synthesis of linear multivariable systems by state feedback, JACC., 468-472 (1964)
[12] Morse, A. S.; Wonham, W. M., Status of noninteracting control, IEEE Trans. Aut. Control, AC-16, 651-669 (1971)
[13] Wolovich, W. A., (Linear Multivariable Control (1974), Springer-Verlag: Springer-Verlag New York) · Zbl 0291.93002
[14] Wolovich, W. A.; Falb, P. L., Invariants and canonical forms under dynamic compensation, SIAM J. Control Optimiz., 14, 996-1008 (1976) · Zbl 0344.93019
[15] Zagalak, P.; Lafay, J. F., Decoupling by static state feedback: a polynomial equation approach, (Preprints IFAC Workshop on System Structure and Control. Preprints IFAC Workshop on System Structure and Control, Prague (1989)), 203-208
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.