PRACTICAL -STABILITY FOR IMPULSIVE DYNAMIC SYSTEMS WITH TIME SCALES AND INITIAL TIME DIFFERENCE |
Chen, Weisong
(School of Science, University of Jinan)
Han, Zhenlai (School of Science, University of Jinan) Sun, Shurong (School of Science, University of Jinan) Li, Tongxing (School of Control Science and Engineering, Shandong University) |
1 | O. Akinyele and J. O. Adeyeye, Cone-valued Lyapunov functions and stbility of hybrid systems, Dyn. Contin. Discrete Impulse. Syst. Math. Anal. 8(2001), 203-214. |
2 | A. A. Martynyuk and Zhenqi Sun, Practical Stability and Applications, Science Press, Beijing, 2004. |
3 | X. Song, S. Li and A. Li, Practical stability of nonlinear differential equation with initial time difference, Appl. Math. Comput. 203(2008), 157-162. DOI ScienceOn |
4 | V. Lakshmikantham and S. Leela, Cone-valued Lyapunov function, Math. Nonlinear Anal. 1(1977), 215-222. DOI ScienceOn |
5 | X. Song, S. Li and A. Li, Practical stability of nonlinear differential equation with initial time difference, Appl. Math. Comput. 203(2008), 157-162. DOI ScienceOn |
6 | V. Lakshmikantham and X. Liu, Impulsive hybrid systems and stability theory, Int. J. Nonlinear Differential Equations 5(1999), 9-17. |
7 | A. Li, E. Feng and S. Li, Stability and boundedness criteria for nonlinear differential systems relative to initial time difference and applications, Int. J. Nonlinear Differential Equations 10(2009), 1073-1080. |
8 | W. Chen, Z. Han, P. Zhao and C. Zhang, Practical -stability of nonlinear differential system with initial time difference, Proceedings of the 7th Conference on Biological Dynamic System and Stability of Differential Equation, World Academic Press Chongqing, China, 2010, 875-878. |
9 | F. A. McRae, Perturbing Lyapunov functions and stability criteria initial time difference, Appl. Math. Comput. 117(2001), 313-320. DOI |
10 | P. Wang and M. Wu, Practical -stabilty of impulsive dynamic systems on time scales, Appl. Math. Lett. 20(2007), 651-658. DOI ScienceOn |
11 | P. Wang and X. Liu, -Stabilty of hybrid impulsive dynamic systems on time scales, J. Math. Anal. Appl. 334(2007), 1220-1231. DOI ScienceOn |
12 | W. Chen, Z. Han, S. Sun and T. Li, -stability of discrete hybrid system with initial time difference, World Congress on Intelligent Control and Automation, World Academic Press Jinan, China, 2010, 2113-2117. |
13 | V. Lakshmikantham, S.Sivasundaram and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Dordrecht, 1996. |
14 | V. Lakshmikantham, Practical stbility of hybrid impulsive dynamic systemsPractical stbility of hybrid impulsive dynamic systems, Int. J. Hybr. Syst. 1 (2001), 67-68. |
15 | E. P. Akpan and O. Akinyele, On the -stabilty of comparson differential systems, J. Math. Anal. Appl. 164(1992), 307-324. DOI |
16 | H. Zhao and E. Feng, Stability of impulsive control systems with variable times, J. Appl. Math. Comput. 23(2007), 345-352. DOI |
17 | C. Yakar and S. G. Deo, Variation of parameters formulae with initial time difference for linear integrodifferential equations, Applicable Analysis 85(2005), 333-343. |
18 | C. Yakar and M. D. Shaw, Practical stability in terms of two measures with initial time difference , Nonlinear Anal. TMA. 71(2009), e781-e785. DOI ScienceOn |