Coupled polynomial equations for LQ control synthesis and an algorithm for solution. (English) Zbl 0787.93029

Summary: The polynomial equation approach can be used to solve a variety of important control problems. The approach leads to the requirement to solve linear polynomial equations. We present a new algorithm for the numerical solution of a general coupled pair of linear polynomial equations. The algorithm is based upon the method of polynomial reductions. Theoretically, solving the coupled equations together enhances the numerical robustness of the equation solution. The algorithm finds a specific and unique minimal degree solution of the equations. The general couple of equations studied is representative of a number of problems in linear control theory, and the minimal degree solution usually corresponds to an optimizing solution of the control problem.


93B50 Synthesis problems
Full Text: DOI


[1] DOI: 10.1137/0318045 · Zbl 0505.93016
[2] DOI: 10.1007/BFb0042749
[3] HUNT K. J., International Journal of Control 49 pp 373– (1989)
[4] DOI: 10.1080/00207178708933981 · Zbl 0635.93021
[5] JEZEK J., Kyberne-tika 18 pp 505– (1982)
[6] JEZEK J., Proceedings of the IFAC World Congress (1987)
[7] KAILATH T., Linear Systems (1980)
[8] KUCERA V., Discrete Linear Control The Polynomial Equation Approach (1979) · Zbl 0432.93001
[9] KUCERA V., Proceedings of the UK-Czech Seminar on Adaptive Control (1990)
[10] NAGY I., Proceedings of IFAC Workshop on Adaptive Systems in Control and Signal Processing (1986)
[11] DOI: 10.1109/TAC.1982.1102933 · Zbl 0488.93066
[12] VOLGIN L. N., The Elements of the Theory of Controllers (1962)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.