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

Dong Hwan Lee, Jin Bae Park, Young Hoon Joo

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)778-785
Number of pages8
JournalSystems and Control Letters
Volume60
Issue number9
DOIs
Publication statusPublished - 2011 Sep

Bibliographical note

Funding Information:
The authors would like to thank the Associate Editor and the anonymous Reviewers for their careful reading and constructive suggestions. This work was supported by the National Research Foundation (NRF) of Korea grant funded by the Korea goverment(MEST) (No.: R01-2008-000-20844-0 ).

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering

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