NDLI: Characteristic Frequencies, Polynomial-Exponential Trajectories, and Linear Exact Modeling with Multidimensional Behaviors

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Zerz, Eva
Copyright Year	2005
Abstract	The characteristic frequencies of a linear, shift-invariant multidimensional behavior correspond to its nonzero exponential trajectories. The set of polynomial-exponential trajectories belonging to a fixed characteristic frequency of a behavior is investigated: A test is derived for determining whether this space is finite-dimensional, and if so, a basis is constructed. If it is infinite-dimensional, one considers only the polynomial-exponential trajectories up to a certain degree of the polynomial part, and a characterization is given of the asymptotic growth of the dimensions of these spaces as the degree bound tends to infinity. A dual problem is concerned with linear exact modeling, that is, the construction of the so-called most powerful unfalsified model (MPUM): Given a finite set of polynomial-exponential trajectories, the goal is to construct a behavior that contains the data and as little else as possible.
Starting Page	1148
Ending Page	1163
Page Count	16
File Format	PDF
ISSN	03630129
DOI	10.1137/S0363012904441738
e-ISSN	10957138
Issue Number	3
Volume Number	44
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	behavioral approach Linear systems General theory polynomial ideals and modules Mathematical modeling Algebraic methods multidimensional systems linear PDE with constant coefficients Systems governed by partial differential equations
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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