«Automation and Informatization of the fuel and energy complex»

One criterion for the complete reachability of linear control systems

UDC: 681.5:622.276+622.279
DOI: 10.33285/0132-2222-2021-11(580)-51-54

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: control system, feedback, complete reachability, canonical form, matrix spectrum

Annotation:

The class of linear dynamic control systems is a mathematical scheme widely used for modeling real objects of the oil and gas industry. The article considers the criterion of complete reachability of linear controlled systems used in solving the so-called pole placement problem for these systems, based on the results of American mathematicians R. Hermann and K. Martin. Their approach uses the apparatus of algebraic geometry and, despite being unconstructive, is very interesting and promising from the point of view of applying methods of algebraic geometry in systems theory.

Bibliography:

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2. Hermann R., Martin C.F. Applications of Algebraic Geometry to Systems Theory – Part 1 // IEEE Transaction on Automatic Control. – 1977. – Vol. 22, Issue 1. – P. 19–25. – DOI: 10.1109/TAC.1977.1101395
3. Falb P. Methods of Algebraic Geometry in Control Theory: Part I. Scalar Linear Systems and Affine Algebraic Geometry. – Boston: Birkhäuser, 1990. – VIII, 204 p.