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Controllability of difference equations| old_uid | 16870 |
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| title | Controllability of difference equations |
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| start_date | 2018/12/06 |
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| schedule | 14h-15h30 |
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| online | no |
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| details | Séminaire du département Parole et Cognition |
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| summary | Difference equations are useful tools in the analysis of some hyperbolic PDEs, in particular systems of PDEs on networks, since they provide a handy representation of some simple dynamics. In this talk, we analyse the controllability of a linear difference equation with finitely many delays. Three notions of controllability are considered: relative, approximate, and exact. We prove that relative controllability is characterized by a necessary and sufficient condition expressed in terms of some coefficients computed inductively from the matrices defining the system. Our criterion generalizes the classical Kalman controllability criterion and one can also provide an upper bound on the maximal controllability time. We then consider approximate and exact controllability in L^2. We provide a complete characterization for 2-dimensional systems with two delays and a scalar control, which corresponds to the first non-trivial situation. It illustrates most difficulties in the analysis and the subtleties of the controllability criterion one obtains. We also relate these controllability properties to approximate and exact controllability to constants. Our approach relies on a suitable representation formula for solutions, which had already been used in a previous work in the stability analysis of difference equations. Part of results of this talk were obtained in collaboration with Y. Chitour and M. Sigalotti. |
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| responsibles | Meyer, Ito |
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