Homogeneous dynamic systems theory

Abstract

In this paper we introduce homogeneous dynamical systems and study many of its important properties. Specifically, we introduce controllability problems and show that a homogeneous dynamical system is controllable in between two states, iff the two states are in the same orbit of a Riccati Flow. We consider observability problems and generalize earlier known 'Popov Belevitch Hautus' rank test for this class of problems. We also obtain observability criterion of a homogeneous dynamical System in the presence of a control input. We introduce realizability problems and derive a suitable generalization of the Hankel-Rank type condition, to test for the minimality of a realization. Finally we. introduce parameter identification problems and explicitly derive identifiability criterion for an important class of homogeneous system.