Taiwanese Journal of Mathematics


Zhi-Qiang Zhu

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This paper is concerned with the study of controllability for a class of multi-valued functional differential systems with impulses and delayed control. By making use of fixed point theorem for multi-valued maps, we prove that our system is completely controllable. The result is obtained in the sense of Carathéodory, and without the requirement that the linear part is controllable.

Article information

Taiwanese J. Math., Volume 18, Number 5 (2014), 1377-1387.

First available in Project Euclid: 10 July 2017

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Zentralblatt MATH identifier

Primary: 34K09: Functional-differential inclusions 34K35: Control problems [See also 49J21, 49K21, 93C23] 34K45: Equations with impulses

multi-valued map functional differential system impulse controllability fixed point


Zhu, Zhi-Qiang. IMPULSIVE CONTROLLABILITY OF MULTI-VALUED FUNCTIONAL DIFFERENTIAL SYSTEMS. Taiwanese J. Math. 18 (2014), no. 5, 1377--1387. doi:10.11650/tjm.18.2014.2242. https://projecteuclid.org/euclid.twjm/1499706517

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  • M. Benchohra and A. Ouahab, Impulsive neutral functiaonl differential inlcusions with variable times, Electron. J. Differential Equations, 2003(67) (2003), 12 pp.
  • B. C. Dhange, A. Boucherif and S. K. Ntouyas, On perodic boundary value prblems of first-order perturbed impulsive differential inclusions, Electron. J. Differential Equations, 2004(84) (2004), 9 pp.
  • B. C. Dhange, A general multi-valued hybrid fixed point theorem and perturbed differential inclusions, Nonlinear Anal., 64 (2006), 2747-2772.
  • L. Górniewicz, S. K. Ntouyas and D. O'Regan, Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces, Rep. Math. Phys., 56 (2005), 437-470.
  • Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer, Dordecht, Boston, London, 1997.
  • A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys., 13 (1965), 781-786.
  • X. Liu and A. R. Willms, Impulsive controllability of linear dynamic systems with applications to maneuvers of spacecraft, Math. Probl. in Eng., 2(4) (1996), 277-299.
  • M. Martelli, A Rothes type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital., 4(3) (1975), 70-76.
  • S. K. Ntouyas, Existence results for impulsive partial neutral functional differential inclusions, Electron, J. Differential Equations, 2005(30) (2005), 11 pp.
  • J. J. Nieto and D. O'Regan, Variational approach to impulsive differential equations, Nonlinear Anal.: Real Word Appl., 10(2) (2009), 680-690.
  • J. J. Nieto and C. C. Tisdell, On exact controllability of first-order impulsive differential equations, Adv. Difference Equ. 2010, (2010), Article ID 136504, 9 papges, doi 10.1155/2010/136504.
  • Z. Q. Zhu and Q. W. Lin, Exact controllability of semilinear systems with impulses, Bull. Math. Anal. Appl., 4(1) (2012), 157-167.