Groebner bases for designing dynamical systems

Abstract

The design or synthesis of systems exhibiting a prescribed trajectory is presented in this paper. The design process is based on algebraic concepts, and it relies heavily on the use of Groebner bases. It is assumed that both the trajectory and its dynamics can be represented as algebraic relationships between the variables of the system and their first derivatives. The method yields a dynamical systems with the desired behavior as one of its many solutions.