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Generic pole assignability, structurally constrained controllers and unimodular completion

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Title Generic pole assignability, structurally constrained controllers and unimodular completion
 
Creator KALAIMANI, RK
BELUR, MN
SIVASUBRAMANIAN, S
 
Subject Structural controllability
Behavioral approach
Structurally fixed modes
DM decomposition
Perfect matching
Generic Smith normal form
Elementary bipartite graph
FIXED MODES
DECENTRALIZED CONTROL
CONTROL-SYSTEMS
FORM
 
Description In this paper we assume dynamical systems are represented by linear differential-algebraic equations (DAEs) of order possibly higher than one. We consider a structured system of DAEs for both the to-be-controlled plant and the controller. We model the structure of the plant and the controller as an undirected and bipartite graph and formulate necessary and sufficient conditions on this graph for the structured controller to generically achieve arbitrary pole placement. A special case of this problem also gives new equivalent conditions for structural controllability of a plant. Use of results in matching theory, and in particular, 'admissibility' of edges and 'elementary bipartite graphs', make the problem and the solution very intuitive. Further, our approach requires standard graph algorithms to check the required conditions for generic arbitrary pole placement, thus helping in easily obtaining running time estimates for checking this. When applied to the state space case, for which the literature has running time estimates, our algorithm is faster for sparse state space systems and comparable for general state space systems. The solution to the above problem also provides a necessary and sufficient condition for the following matrix completion problem. Given a structured rectangular polynomial matrix, when can it be completed to a unimodular matrix such that the additional rows that are added during the completion process are constrained to have zeros at certain locations. (C) 2013 Elsevier Inc. All rights reserved.
 
Publisher ELSEVIER SCIENCE INC
 
Date 2014-10-16T07:11:12Z
2014-10-16T07:11:12Z
2013
 
Type Article
 
Identifier LINEAR ALGEBRA AND ITS APPLICATIONS, 439(12)4003-4022
0024-3795
1873-1856
http://dx.doi.org/10.1016/j.laa.2013.10.004
http://dspace.library.iitb.ac.in/jspui/handle/100/15519
 
Language en