Approximate controllability of impulsive differential equations with state-dependent delay

International Journal of Control

Volumn 83, Issue 2, 2010, Pages 387-393

  Sakthivel, R ^a   Anandhi, E R ^b  

^a Sungkyunkwan University   (South Korea)

^b MEDICAL UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Approximate controllability; Nonlinear impulsive systems; State dependent delay

Indexed keywords

ABRUPT CHANGE; APPROXIMATE CONTROLLABILITY; ENGINEERING SCIENCE; EVOLUTION PROCESS; IMPULSIVE DIFFERENTIAL EQUATION; NONLINEAR IMPULSIVE DIFFERENTIAL SYSTEMS; NONLINEAR IMPULSIVE SYSTEMS; REAL-WORLD PROBLEM; SEMI-GROUP THEORY; STATE-DEPENDENT DELAY; SUFFICIENT CONDITIONS; SYSTEM MODELS;

DIFFERENTIAL EQUATIONS; LINEAR CONTROL SYSTEMS; MODEL STRUCTURES; NONLINEAR EQUATIONS;

CONTROLLABILITY;

EID: 76249115782     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170903171348     Document Type: Article

References (24)

1. Anandhi, E.R., and Voit, E.O. (2005), 'Controllability of Non-linear Biochemical Systems', Mathematical Biosciences, 196, 99-123.
2. Arino, O., Habid, ML., and de la Parra, RB. (1998), 'A Mathematical Model of Growth of Population of Fish in the Larval Stage: Density-dependence Effects', Mathematical Biosciences, 150, 1-20.
3. Balasubramaniam, P., Dauer, J.P., and Loganathan, C. (2002), 'Local Controllability of Functional Integrodifferential Equation in Banach Space', Journal of Optimization Theory and Applications, 114, 273-286.
4. Balachandran, K., and Sakthivel, R. (2001), 'Controllability of Functional Semilinear Integrodifferential Systems in Banach Spaces', Journal of Mathematical Analysis and Applications, 255, 447-457. (Pubitemid 33377561)
5. Ballinger, G., and Liu, X. (2003), 'Boundness for Impulsive Delay Differential Equations and Applications to Population Growth Models', Nonlinear Analysis, 53, 1041-1062.
6. Benchohra, M., Gorniewicz, L., Ntouyas, S.K., and Ouahab, A. (2006), 'Controllability Results for Nondensely Defined Semilinear Functional Differential Equations', Zeitschrift für Analysis und ihre Anwendungen, 25, 311-325.
7. Chalishajar, D.N., George, R.K., and Nandakumaran, A.K. (2007), 'Exact Controllability of the Third Order Nonlinear Dispersion Equation', Journal of Mathematical Analysis and Applications, 332, 1028-1044.
8. Chang, Y.K. (2007), 'Controllability of Impulsive Functional Differential Systems with Infinite Delay in Banach Spaces', Chaos, Solitons & Fractals, 33, 1601-1609.
9. Chang, Y.K., Li, W.T., and Nieto, J.J. (2007), 'Controllability of Evolution Differential Inclusions in Banach Spaces', Nonlinear Analysis, 67, 623-632.
10. Dauer, J.P., and Mahmudov, N.I. (2002), 'Approximate Controllability of Semilinear Functional Equations in Hilbert Spaces', Journal of Mathematical Analysis and Applications, 273, 310-327.
11. Gao, S., Chen, L., Nieto, J.J., and Torres, A. (2006), 'Analysis of a Delayed Epidemic Model with Pulse Vaccination and Saturation Incidence', Vaccine, 24, 6037-6045.
12. Gao, C., Li, K., Feng, E., and Xiu, Z. (2006), 'Nonlinear Impulsive System of Fed-batch Culture in Fermentative Production and Its Properties', Chaos Solitons & Fractals, 28, 271-277.
13. Gorniewicz, L., Ntouyas, S.K., and O'Regan, D. (2005), 'Controllability of Semilinear Differential Equations and Inclusions via Semigroup Theory in Banach Spaces', Reports on Mathematical Physics, 56, 437-470.
14. Hernandez, E., Sakthivel, R., and Tanaka, S.A. (2008), 'Existence Results for Impulsive Evolution Differential Equations with State-dependent Delay', Electronic Journal of Differential Equations, 28, 11.
15. Hino, Y., Murakami, S., and Naito, T. (1991), Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics (Vol. 1473), Berlin: Springer-Verlag.
16. Kartsatos, AC. (2005), 'On the Approximate K-controllability of Nonlinear Systems in Banach Spaces', Nonlinear Analysis, Theory Methods & Applications, 62, 315-344.
17. Li, ML., Wang, MS., and Zhang, FQ. (2006), 'Controllability of Impulsive Functional Differential Systems in Banach Spaces', Chaos, Solitons & Fractals, 29, 175-181.
18. Liu, B. (2005), 'Controllability of Impulsive Neutral Functional Differential Inclusions with Infinite Delay', Nonlinear Analysis, 60, 1533-1552.
19. Mahaffy, JM., Belair, J., and Mackey, MC. (1998), 'Hematopoietic Model with Moving Boundary Condition and State Dependent Delay: Applications in Erythropoiesis', Journal of Theoretical Biology, 190, 135-146.
20. Mahmudov, N.I. (2003), 'Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces', SIAM Journal on Control and Optimization, 42, 1604-1622.
21. Mahmudov, N.I. (2008), 'Approximate Controllability of Evolution Systems with Nonlocal Conditions', Nonlinear Analysis, 68, 536-546.
22. Naito, K. (1989), 'Approximate Controllability for Trajectories of Semilinear Control Systems', Journal of Optimization Theory and Applications, 60, 57-65.
23. Sakthivel, R., Anthoni, S.M., and Kim, J.H. (2005), 'Existence and Controllability Result for Semilinear Evolution Integrodifferential Systems', Mathematical and Computer Modelling, 41, 1005-1011.
24. Tang, S., and Chen, L. (2002), 'Density-dependent Birth Rate, Birth Pulses and Their Population Dynamic Consequences', Journal of Mathematical Biology, 44, 185-199.