Applications of Constructive Algebra to Control Problems
Krister Forsman · 1990
Constructive algebra consists in solving algebraic problems algorithmically. This thesis consists of two parts; In the first part constructive methods in commutitaive and differential algebra are presented and then compared. In the second part is is showed how constructive algebraic methods, and in particular Grobner bases, can be applied to some problems in control theory. These problems include design of regulators for linear systems, finding maximal level surfaces of Lyapunov functions and solving the equations that arise in the harmonic balancing method. The methods proposed are illustrated by concrete examples.