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 language | English |
|---|---|
| Pages (from-to) | 778-785 |
| Number of pages | 8 |
| Journal | Systems and Control Letters |
| Volume | 60 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2011 Sep 1 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science(all)
- Mechanical Engineering
- Electrical and Electronic Engineering
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Fundamental connections among the stability conditions using higher-order time-derivatives of Lyapunov functions for the case of linear time-invariant systems. / Lee, Dong Hwan; Park, Jin Bae; Joo, Young Hoon.
In: Systems and Control Letters, Vol. 60, No. 9, 01.09.2011, p. 778-785.Research output: Contribution to journal › Article
TY - JOUR
T1 - Fundamental connections among the stability conditions using higher-order time-derivatives of Lyapunov functions for the case of linear time-invariant systems
AU - Lee, Dong Hwan
AU - Park, Jin Bae
AU - Joo, Young Hoon
PY - 2011/9/1
Y1 - 2011/9/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=80051795409&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2011.06.003
DO - 10.1016/j.sysconle.2011.06.003
M3 - Article
VL - 60
SP - 778
EP - 785
JO - Systems and Control Letters
JF - Systems and Control Letters
SN - 0167-6911
IS - 9
ER -