Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
696219 | Automatica | 2012 | 5 Pages |
Abstract
We prove that a set of smooth trajectories is LTID (i.e., the solution set of a constant coefficient linear differential equation) if and only if it is the direct sum of a linear time-invariant closed controllable part and a linear time-invariant finite-dimensional part. This characterisation does not directly involve derivatives in its formulation. It solves a problem opened by Willems (1991). We also characterise morphisms between LTID sets as linear time-invariant maps which do not increase support.
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Physical Sciences and Engineering
Engineering
Control and Systems Engineering
Authors
Jean-Charles Delvenne,