Abstract
A lattice-type structure is shown to exist in a particular subset of the set of all (A, ℱ)-controlled invariants contained in\(\mathcal{N}\) and containing\(\mathcal{N}\), whereA denotes a linear map inR n; ℱ,\(\mathcal{N}\) are arbitrary subspaces ofR n; andD is an arbitrary subspace ofJ, the maximum (A, ℱ)-controlled invariant contained in\(\mathcal{N}\). In linear system theory, this property can be used for a more direct theoretical and algorithmic approach to constrained controllability and disturbance rejection problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Basile, G., andMarro, G.,Controlled and Conditioned Invariant Subspaces in Linear System Theory, Journal of Optimization Theory and Applications, Vol. 3, pp. 305–315, 1969.
Basile, G., andMarro, G.,L'Invarianza rispetto ai Disturbi Studiata nello Spazio degli Stati, Rendiconti della LXX Riunione Annuale AEI, Paper No. 1-4-01, 1969.
Wonham, W. M., andMorse, A. S.,Decoupling and Pole Assignment in Linear Multivariable Systems: a Geometric Approach, SIAM Journal on Control, Vol. 8, pp. 1–18, 1970.
Morse, A. S., andWonham, W. M.,Decoupling and Pole Assignment by Dynamic Compensation, SIAM Journal on Control, Vol. 8, pp. 317–327, 1970.
Basile, G., andMarro, G.,A State Space Approach to Noninteracting Controls, Ricerche di Automatica, Vol. 1, pp. 68–77, 1970.
Wonham, W. M.,Tracking and Regulation in Linear Multivariable Systems, SIAM Journal on Control, Vol. 11, pp. 424–437, 1973.
Wonham, W. M., andPearson, J. B.,Regulation and Internal Stabilization in Linear Multivariable Systems, SIAM Journal on Control, Vol. 12, pp. 68–77, 1974.
Bonivento, C., Guidorzi, R., andMarro, G.,Parametric Insensitivity and Controlled Invariance, Automatica, Vol. 11, pp. 381–388, 1975.
Schumacher, J. M., (C, A)-Invariant Subspaces: Some Facts and Uses, Vrije Universiteit, Amsterdam, Holland, Report No. 110, 1979.
Akashi, H., andImai, H.,Disturbance Localization and Output Deadbeat Control Through an Observer in Discrete-Time Linear Multivariable Systems, IEEE Transactions on Automatic Control, Vol. AC-24, pp. 621–627, 1979.
Imai, H., andAkashi, H.,Disturbance Localization and Pole Shifting by Dynamic Compensation, IEEE Transactions on Automatic Control, Vol. AC-26, pp. 226–234, 1981.
Willems, J. C.,Almost Invariant Subspaces: an Approach to High-Gain Feedback Design, Part 1, Almost Controlled Invariant Subspaces, IEEE Transactions on Automatic Control, Vol. AC-26, pp. 235–252, 1981.
Basile, G., Hamano, F., andMarro, G.,Some New Results on Unknown Input Observability, Proceedings of the 8th IFAC Congress, Kyoto, Japan, 1981.
Wonham, W. M.,Linear Multivariable Control: a Geometric Approach, Springer-Verlag, New York, New York, 1974.
Kalman, R. E.,On the General Theory of Control Systems, Proceedings of the 1st IFAC Congress, Vol. 1, Butterworths, London, England, 1961.
Basile, G., andMarro, G.,Luoghi Caratteristici dello Spazio degli Stati Relativi al Controllo dei Sistemi Lineari, L'Elettrotecnica, Vol. 55, pp. 1–7, 1968.
Marro, G.,Fondamenti di Teoria dei Sistemi, Patron Editore, Bologna, Italy, 1975.
Morse, A. S.,Structural Invariants of Linear Multivariable Systems, SIAM Journal on Control, Vol. 11, pp. 446–465, 1973.
Molinari, B. P.,A Strong Controllability and Observability in Linear Multivariable Control, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 761–764, 1976.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
Rights and permissions
About this article
Cite this article
Basile, G., Marro, G. Self-bounded controlled invariant subspaces: A straightforward approach to constrained controllability. J Optim Theory Appl 38, 71–81 (1982). https://doi.org/10.1007/BF00934323
Issue Date:
DOI: https://doi.org/10.1007/BF00934323