Colloquium February 19

Date: Thursday, February 19

Time: 16:00 to 17:00

Place: 455 McBryde (Commons Room)

Speaker: Andrey Melnikov of Ben Gurion Univ

Title: Kalman theory of overdetermined 2D systems, invariant in one direction

Abstract: In my thesis (under the supervision of V. Vinnikov) we have studied the class of overdetermined 2D systems, invariant in one direction (say t1). Performing separation of variables one obtains the notion of transfer function. Any transfer function S(λ,t2) has the following properties

  1. S(λ,t2) is analytic at the neighborhood of infinity,
  2. S(λ,t2) is absolutely continuous as a function of t2 for each λ,
  3. S(λ,t2) maps solutions of a certain Linear Differential equation with spectral parameter λ to another one.
It turns out that the spectrum of S(λ,t2) is t2 independent. Notions of controllability, observability and of minimality are defined and as a result basic theorems of the classical Kalman theory can be stated and proved: Kalman decomposition, quasi similarity of minimal systems, etc. The connection between systems and transfer functions will be at the center of my talk. If time permits I will consider some basic constructions of the system theory (projections, cascade decompositions, compression) and the corresponding factorizations of the transfer function. The material of this talk is at http://arXiv.org/abs/0812.3779 (to be submitted shortly).

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