Finite Time Stability of Autonomous Nonsmooth Systems With Time-delays

CHENG Guifang, Ding Zhishuai, MU Xiaowu

Acta Mathematicae Applicatae Sinica ›› 2013, Vol. 0 ›› Issue (1) : 14-22.

PDF(319 KB)
PDF(319 KB)
Acta Mathematicae Applicatae Sinica ›› 2013, Vol. 0 ›› Issue (1) : 14-22. DOI: 10.12387/C2013002

Finite Time Stability of Autonomous Nonsmooth Systems With Time-delays

  • CHENG Guifang1, Ding Zhishuai2,3, MU Xiaowu1
Author information +
History +

Abstract

It is mainly discussed finite time stability of autonomous systems with nonsmooth right-hand sides (in the sense of Filippov solutions) with time-delay. The definition of finite time stability of retarded nonsmooth systems and comparison principle are presented. Based on Filippov differential inclusions and nonsmooth Lyapunov-Krasovkii functional, Lyapunov theorem for finite time stability of retarded nonsmooth systems is shown.

Key words

nonsmooth systems / ratarded systems / Filippov solutions / finite time stability

Cite this article

Download Citations
CHENG Guifang, Ding Zhishuai, MU Xiaowu. Finite Time Stability of Autonomous Nonsmooth Systems With Time-delays. Acta Mathematicae Applicatae Sinica, 2013, 0(1): 14-22 https://doi.org/10.12387/C2013002

References

[1] Haimo V T. Finite Time Controllers. SIAM J. Control Optim., 1986, 24: 760-770
[2] Choura S. Design of Finite-time Settling Regulators for Linear Systems. ASME Journal of DynamicSystems Measurement and Control, 1994, 116: 602-609
[3] Bhat S P, Bernstein D S. Lyapunov Analysis of Finite-time Differential Equations. Proceedings ofthe American Control Conference, Seattle, WA, 1995: 1831-1832
[4] Bhat S P, Bernstein D S. Continuous Finite-time Stabilization of the Translational and RotationalDouble Integrators. IEEE Trans. Automat. Control, 1998, 43: 678-682
[5] Bhat S P, Bernstein D S. Bernstein. Finite-time Stability of Continuous Autonomous Systems. SIAMJ. Control Optim., 2000, 38(3): 751-766
[6] Moulay E, Perruquetti W. Finite Time Stability and Stabilization of a Class of Continuous Systems.J. Math. Anal. Appl., 2006, 323(2): 1430-1443
[7] Hong Y G. Finite-time Stabilization and Stabilizability of a Class of Controllable Systems. Syst.Control Lett., 2002, 46: 231-236
[8] Hong Y G, Wang J, Cheng D Z. Adaptive Finite-time Control of a Class of Uncertain NonlinearSystems. IEEE Trans. Autom. Control, 2006, 51(5): 858-862
[9] Hong Y G, Jiang Z P. Finite-time Stabilization of Nonlinear Systems with Parametric and DynamicUncertainties. IEEE Trans. Autom. Control, 2006, 51(12): 1950-1956
[10] Huang H Q. Finite-time Stabilization and Detection of Nonlinear Systems. A Dissertation for theDegree of PH.D, Case Western Reserve University, 2003
[11] Filippov A F. Differential Equations with Discontinuous Right-hand Side. Amer. Math. Soc.Translations, 1964, 42(2): 199-231
[12] Clarke F, Ledyaev Y, Stern R, and Wolenski P. Nonsmooth Analysis and Control Theory. GraduateTexts in Mathematics. New York: Springer-Verlag, 1998
[13] Shevitz D, Paden B. Lyapunov Stability Theory of Nonsmooth Systems. IEEE Transactions onAutomatic Control, 1994, 39(9): 1910-1914
[14] Bacciotti A, Ceragioli F. Stability and Stabilization of Discontinuous Systems and Nonsmooth Lya-punov Functions. ESAIM Control, Optimisation and Calculus of Variations, 1999, 4: 361-376
[15] Loria A, Panteley E, Nijmeijer H. A Remark on Passivity-based and Discontinuous Control of Uncer-tain Nonlinear Systems. Automatica, 2001, 37: 1481-1487
[16] 慕小武, 程桂芳, 唐风军. 非自治非光滑系统的Matrosov稳定性定理. 应用数学学报, 2007, 30(1): 168-175(Cheng G F, Mu X W, Ding Z S. Uniformly Ultimate Boundedness for a Class of DiscontinuousNonautonomous Systems. Acta Mathematicae Applicatae Sinica, 2007, 30(4): 675-681)
[17] 程桂芳, 慕小武, 丁志帅. 一类不连续非自治系统的一致最终有界性. 应用数学学报, 2007, 30(4): 675-681(Cheng G F, Mu X W, Ding Z S. Uniformly Ultimate Boundedness for a Class of Discontinuous Nonautonomous Systems. Acta Mathematicae Applicatae Sinica, 2007, 30(4): 675-681) [18] Mu XW, Cheng G F, Ding Z S. On Stability of Discontinuous Systems via Vector Lyapunov Functions.Applied Mathematics and Mechanics (English Edition), 2007, 28(12): 1613-1619
[19] Cheng G. F, Mu X W. Finite-time Stability with Respect to a Closed Invariant Set for a Class ofDiscontinuous Systems. Applied Mathematics and Mechanics (English Edition), 2009, 30(8): 1069-1075
[20] Zhang J Y, Shen T L. Functional Differential Inclusion-based Approach to Control of DiscontinuousNonlinear Systems with Time Delay. Mexico: Proceeding of 47th IEEE Conference on Decision andControl, 2008, 5300-5305
[21] Zhang J Y, Shen T L, Jiao X H. Stability and Feedback Design of a Class of Time-delay Systems withDiscontinuity: Functional Differential Inclusion-based Approach. IEE J. Trans. EIS, 2009, 129(6):1108-1114
[22] Zhang J Y, Shen T L, Jiao X H. L2-gain Analysis and Feedback Design for Discontinuous Time-delay Systems Based on Functional Differential Inclusion. Shanghai: Joint 48th IEEE Conference onDecision and Control and 28th Chinese Control Conference, 2009, 5114-5119
PDF(319 KB)

61

Accesses

0

Citation

Detail

Sections
Recommended

/