On the computation of piecewise quadratic Lyapunov functions

A new parametrization of piecewise quadratic functions is presented, aimed for convex optimization of Lyapunov functions. The parametrization ensures continuity of the functions, but is also flexible enough to approximate any continuous function with arbitrary accuracy. A converse Lyapunov theorem i...

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Bibliographic Details
Published inProceedings of the 36th IEEE Conference on Decision and Control Vol. 4; pp. 3515 - 3520 vol.4
Main Authors Johansson, M., Rantzer, A.
Format Conference Proceeding
LanguageEnglish
Published IEEE 1997
Subjects
Control system synthesis
Ear
Level set
Linear systems
Lyapunov method
Nonlinear systems
Performance analysis
Piecewise linear approximation
Stability analysis
State-space methods
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ISBN0780341872
9780780341876
ISSN0191-2216
DOI10.1109/CDC.1997.652393

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Summary:A new parametrization of piecewise quadratic functions is presented, aimed for convex optimization of Lyapunov functions. The parametrization ensures continuity of the functions, but is also flexible enough to approximate any continuous function with arbitrary accuracy. A converse Lyapunov theorem is given, stating that all exponentially stable systems of a certain class will in principle admit a piecewise quadratic Lyapunov function, to be found by the given optimization procedure.
ISBN:0780341872
9780780341876
ISSN:0191-2216
DOI:10.1109/CDC.1997.652393