Abstract
This paper investigates the new stability criteria for the asymptotic stability of time-delay systems via integral inequalities and Jensen inequalities. Firstly, not only the known constant time delay, but also the unknown time-varying delay is considered for the linear system. Secondly, the new delay-dependent Lyapunov–Krasovskii functional based on the double integral inequalities and Jensen inequalities is introduced, such that the linear system with time-delay is asymptotically stable. Thirdly, two classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived, such that the control design conditions are relaxed and computation complexity is reduced. Compared with previous works, the larger feasible solution region and less conservative results are obtained. Finally, some numerical examples are performed to show the effectiveness and advantage of the proposed method.
Highlights
Time delays exist in many dynamic systems, such as the chemical or process control systems, and often result in poor performance and instability [1,2,3,4]
The contributions of this paper are listed as follows: (1) The known constant time delay h > 0 and the unknown time-varying delay 0 ≤ h1 ≤ h(t) ≤ h2 are both considered in the linear system
(2) The delay-dependent Lyapunov–Krasovskii functional based on the double integral inequalities and Jensen inequalities is introduced, the linear system is asymptotically stable and the larger feasible solution region is obtained
Summary
Time delays exist in many dynamic systems, such as the chemical or process control systems, and often result in poor performance and instability [1,2,3,4]. (2) The delay-dependent Lyapunov–Krasovskii functional based on the double integral inequalities and Jensen inequalities is introduced, the linear system is asymptotically stable and the larger feasible solution region is obtained. Lemma 2 For a given matrix R > 0 and a differentiable function x : [a, b] → Rn, the following double integral inequality holds: bb xT (s)Rx(s) ds du ≥ 2Ω4T RΩ4 + 4Ω5T RΩ5 + 6Ω6T RΩ6,. Lemma 3 ([30]) For a given matrix R > 0 and a differentiable function φ : [a, b] → Rn, the following inequality holds: IRq(φ). Lemma 5 For a given matrix R > 0 and a differentiable function φ : [a, b] → Rn, the following Jensen inequality holds: ζ1 ζ2.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
