The autonomous regulator problem for linear, time-delay systems: A geometric approach

The aim of this paper is to show the applicability of geometric techniques to a regulation problem for linear, time-delay systems. Given a plant whose dynamics equations include delays, the problem we consider consists in finding a feedback regulator which guarantees asymptotic stability of the regulation loop and asymptotic command following of the reference signal generated by an exosystem, for any initial condition of the overall system. By associating to the time-delay plant a corresponding abstract system with coefficients in a ring, it is possible to place our investigation in a finite dimensional algebraic context, where intuition and results obtained in the classical case, that is without delays, may be exploited.