On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form

In this note, the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices A/sub 1/ and A/sub 2/ are in companion form is considered. It is shown that a necessary and...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2003-04, Vol.48 (4), p.618-621
Main Authors: Shorten, R.N., Narendra, K.S.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Computer science
control theory
systems
Control theory. Systems
Eigenvalues
Eigenvalues and eigenfunctions
Exact sciences and technology
Linear algebra
Linear matrix inequalities
Linear systems
Lyapunov functions
Lyapunov method
Mathematical analysis
Matrices
Matrix methods
Miscellaneous
Polynomials
Stability
Sufficient conditions
Symmetric matrices
Time domain analysis
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Summary:In this note, the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices A/sub 1/ and A/sub 2/ are in companion form is considered. It is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product A/sub 1/A/sub 2/ does not have an eigenvalue that is real and negative. Examples are presented to illustrate the result.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2003.809795