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Positive Forms and Stability of Linear Time-Delay Systems

Abstract:
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on the space of continuous functions. We give an explicit parametrization of a sequence of finite-dimensional subsets of the cone of positive Lyapunov functions using positive semidefinite matrices. This allows stability analysis of linear time-delay systems to be formulated as a semidefinite program.
Publication status:
Published

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Publisher copy:
10.1137/070706999

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Institution:
University of Oxford
Division:
MPLS
Department:
Engineering Science
Role:
Author
Volume:
47
Pages:
3237-3258
Host title:
SIAM J. Control and Optimization
Publication date:
2007-07-02
DOI:
ISSN:
0191-2216
Source identifiers:
64655
ISBN:
9781424401703
Keywords:
Pubs id:
pubs:64655
UUID:
uuid:c4436b44-a186-4c2d-9518-9514ece4c487
Local pid:
pubs:64655
Deposit date:
2012-12-19

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