Title :
A characterization of solution sets of LTI differential equations
Author :
Delvenne, Jean-Charles ; Ivanov, Tzvetan
Author_Institution :
Center for Syst. Eng. & Appl. Mech. (CESAME), Univ. Catholique de Louvain, Louvain-la-Neuve, Belgium
Abstract :
We prove that a controllable set of smooth trajectories is the solution set of a constant coefficient linear differential equation if and only if it is linear, time invariant and closed. This characterization does not involve derivatives in its formulation. It solves a problem opened by Willems.
Keywords :
controllability; linear differential equations; LTI differential equation; constant coefficient linear differential equation; smooth trajectories; Circuits; Control theory; Convergence; Differential equations; Kalman filters; State-space methods; Systems engineering and theory; Topology; Transfer functions; Voltage;
Conference_Titel :
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2009.5399519
