Computing the radius of controllability for state space systems

In this paper, we discuss the problem of computing the nearest uncontrollable system to a given control system represented by a matrix pair ( A , B ) . In order to do so, we construct a sequence of structured matrices from given system matrices A and B . Controllability of the pair ( A , B ) is equi...

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Bibliographic Details
Published in:Systems & control letters 2012-02, Vol.61 (2), p.327-333
Main Authors: Khare, Swanand R., Pillai, Harish K., Belur, Madhu N.
Format: Article
Language:English
Subjects:
Affinely structured matrices
Applied sciences
Approximation
Computation
Computer science
control theory
systems
Control system analysis
Control systems
Control theory. Systems
Controllability
Equivalence
Exact sciences and technology
Mathematical analysis
Matrices
Modelling and identification
Radius of controllability
Structured Low Rank Approximation (SLRA)
Structured matrices
Structured Total Least Norm (STLN)
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Summary:In this paper, we discuss the problem of computing the nearest uncontrollable system to a given control system represented by a matrix pair ( A , B ) . In order to do so, we construct a sequence of structured matrices from given system matrices A and B . Controllability of the pair ( A , B ) is equivalent to a condition on the null-space dimension of an appropriate matrix in this sequence. We show that the dimension of the reachability space is also related to the above condition. Further, it is shown that the nearest Structured Low Rank Approximation (SLRA) of this structured matrix corresponds to a nearest uncontrollable system to the pair ( A , B ) .
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2011.11.012