Applications of algebraic geometry to systems theory, part II: Feedback and pole placement for linear Hamiltonian systems
- 1 June 1977
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 65 (6) , 841-848
- https://doi.org/10.1109/proc.1977.10580
Abstract
In this paper we show that the methods of algebraic geometry can be used to study the linear optimal regulator problem. It is shown that under certain conditions almost any system is obtainable by optimal feedback. To do this involves developing general techniques for studying feedback in systems, using methods from the theory of multivariable polynomials. The linear quadratic regulator problem can be viewed as a feedback problem, with feedback preserving the linear symplectic group. New general techniques are developed that might be useful for other systems-theoretic problems; to enhance the possibility of such utilization, a new simpler proof of main "almost-ontoness" theorem from algebraic geometry, using the classical theory of resultants, is given in an Appendix.Keywords
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