Journal
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
Volume 31, Issue 15, Pages 7361-7371Publisher
WILEY
DOI: 10.1002/rnc.5682
Keywords
cubic function; negative-definiteness condition; stability; time-delay system
Funding
- Fundamental Research Funds for National Universities, China University of Geosciences (Wuhan)
- Hubei Provincial Natural Science Foundation of China [2019CFA040]
- National Natural Science Foundation of China [61873347, 61973284, 62022074]
- 111 project [B17040]
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This article investigates the delay-dependent stability of systems with a time-varying delay and proposes a negative-definiteness lemma for cubic functions to achieve stability analysis without introducing additional decision variables. By constructing an LKF with more delay information, a delay-dependent stability criterion is derived, and the contributions of the proposed lemma and criterion are demonstrated through two examples.
This article studies the delay-dependent stability of systems with a time-varying delay. To get a stability criterion described as linear matrix inequalities (LMIs) from a positive definite Lyapunov-Krasovskii functional (LKF), the negative-definiteness condition, guaranteeing the negative definiteness of the derivative of the LKF, is necessary. This article proposes a negative-definiteness lemma for the cubic function with respect to the time-varying delay, which achieves the negative-definiteness requirement without introducing any decision variable and extending the size of the LMIs contained in a stability criterion. Then benefiting from this lemma, an LKF with more delay information is constructed and applied to the stability analysis. After that, a delay-dependent stability criterion is derived based on the LKF and the negative-definiteness lemma. Finally, the contribution of the proposed lemma and the stability criterion is demonstrated with two examples.
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