A characterization of solution sets of LTI differential equations

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 [1].

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Jean-Charles Delvenne, Tzvetan Ivanov
• Keywords: CDC 2009, Control Systems, Controllable Set, Smooth Trajectories