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Causal and stable input/output structures on multidimensional behaviors

DSpace at IIT Bombay

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Title Causal and stable input/output structures on multidimensional behaviors
 
Creator WOOD, J
SULE, VR
ROGERS, E
 
Subject linear-systems
time-controllability
stabilization
extension
autonomy
modules
stability
causality
partial differential equations
multidimensional systems
behavioral approach
hyperbolic systems
input/output structures
time-autonomy
 
Description In this work we study multidimensional (nD) linear differential behaviors with a distinguished independent variable, called "time." We define in a natural way causality and stability of input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonstrating that causality is equivalent to a property of the transfer matrix which is essentially hyperbolicity of the P-c operator defining the behavior (B-c)(0,y). We also quote results which in effect characterize time-autonomy for the general systems case. Stability is likewise characterized by a property of the transfer matrix. We prove this result for the 2D case and for the case of a single equation; for the general case it requires solution of an open problem concerning the geometry of a particular set in C-n. In order to characterize input/output stability we also develop new results on inclusions of kernels, freeness of variables, and closure with respect to S, S' and associated spaces, which are of independent interest. We also discuss stability of autonomous behaviors, which we believe to be governed by a corresponding condition.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T04:32:58Z
2011-12-26T12:58:24Z
2011-12-27T05:48:16Z
2011-08-29T04:32:58Z
2011-12-26T12:58:24Z
2011-12-27T05:48:16Z
2004
 
Type Article
 
Identifier SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 43(4), 1493-1520
0363-0129
http://dx.doi.org/10.1137/S0363012903429979
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11959
http://hdl.handle.net/10054/11959
 
Language en