Fundamental connections among the stability conditions using higher-order time-derivatives of Lyapunov functions for the case of linear time-invariant systems

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It has already been recognized that looking for a positive definite Lyapunov function such that a high-order linear differential inequality with respect to the Lyapunov function holds along the trajectories of a nonlinear system can be utilized to assess asymptotic stability when the standard Lyapunov approach examining only the first derivative fails. In this context, the main purpose of this paper is, on one hand, to theoretically unveil deeper connections among existing stability conditions especially for linear time-invariant (LTI) systems, and from the other hand to examine the effect of the higher-order time-derivatives approach on the stability results for uncertain polytopic LTI systems in terms of conservativeness. To this end, new linear matrix inequality (LMI) stability conditions are derived by generalizing the concept mentioned above, and through the development, relations among some existing stability conditions are revealed. Examples illustrate the improvement over the quadratic approach.
Publisher
ELSEVIER
Issue Date
2011-09
Language
English
Article Type
Article
Citation

SYSTEMS & CONTROL LETTERS, v.60, no.9, pp.778 - 785

ISSN
0167-6911
DOI
10.1016/j.sysconle.2011.06.003
URI
http://hdl.handle.net/10203/272981
Appears in Collection
EE-Journal Papers(저널논문)
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