Asymptotic behaviors of solutions of a class of time-varying differential equations

References

[1] A. Ben Abdallah, M. Dlala and M. A. Hammami, Exponential stability of perturbed nonlinear systems, Nonlinear Dyn. Syst. Theory 5 (2005), no. 4, 357–367. Search in Google Scholar

[2] A. Ben Abdallah, M. Dlala and M. A. Hammami, A new Lyapunov function for stability of time-varying nonlinear perturbed systems, Systems Control Lett. 56 (2007), no. 3, 179–187. 10.1016/j.sysconle.2006.08.009Search in Google Scholar

[3] A. Benabdallah, I. Ellouze and M. A. Hammami, Practical stability of nonlinear time-varying cascade systems, J. Dyn. Control Syst. 15 (2009), no. 1, 45–62. 10.1007/s10883-008-9057-5Search in Google Scholar

[4] A. Benabdallah, I. Ellouze and M. A. Hammami, Practical exponential stability of perturbed triangular systems and a separation principle, Asian J. Control 13 (2011), no. 3, 445–448. 10.1002/asjc.325Search in Google Scholar

[5] A. Benabdallah and M. A. Hammami, On the output feedback stability for non-linear uncertain control systems, Internat. J. Control 74 (2001), no. 6, 547–551. 10.1080/00207170010017383Search in Google Scholar

[6] B. Ben Hamed, I. Ellouze and M. A. Hammami, Practical uniform stability of nonlinear differential delay equations, Mediterr. J. Math. 8 (2011), no. 4, 603–616. 10.1007/s00009-010-0083-7Search in Google Scholar

[7] B. Ben Nasser, K. Boukerrioua, M. Defoort, M. Djemai, M. A. Hammami and T.-M. Laleg-Kirati, Sufficient conditions for uniform exponential stability and h-stability of some classes of dynamic equations on arbitrary time scales, Nonlinear Anal. Hybrid Syst. 32 (2019), 54–64. 10.1016/j.nahs.2018.10.009Search in Google Scholar

[8] T. Caraballo, M. A. Hammami and L. Mchiri, Practical exponential stability of impulsive stochastic functional differential equations, Systems Control Lett. 109 (2017), 43–48. 10.1016/j.sysconle.2017.09.009Search in Google Scholar

[9] A. Chaillet and A. Loría, Necessary and sufficient conditions for uniform semiglobal practical asymptotic stability: Application to cascaded systems, Automatica J. IFAC 42 (2006), no. 11, 1899–1906. 10.1016/j.automatica.2006.05.028Search in Google Scholar

[10] M. Corless, Guaranteed rates of exponential convergence for uncertain systems, J. Optim. Theory Appl. 64 (1990), no. 3, 481–494. 10.1007/BF00939420Search in Google Scholar

[11] H. Damak, M. A. Hammami and B. Kalitine, On the global uniform asymptotic stability of time-varying systems, Differ. Equ. Dyn. Syst. 22 (2014), no. 2, 113–124. 10.1007/s12591-012-0157-zSearch in Google Scholar

[12] M. Dlala and M. A. Hammami, Uniform exponential practical stability of impulsive perturbed systems, J. Dyn. Control Syst. 13 (2007), no. 3, 373–386. 10.1007/s10883-007-9020-xSearch in Google Scholar

[13] A. Dorgham, M. Hammi and M. A. Hammami, Asymptotic behavior of a class of perturbed differential equations, Ukrainian Math. J. 73 (2021), no. 5, 731–745. 10.1007/s11253-021-01956-5Search in Google Scholar

[14] I. Ellouze and M. A. Hammami, A separation principle of time-varying dynamical systems: A practical stability approach, Math. Model. Anal. 12 (2007), no. 3, 297–308. 10.3846/1392-6292.2007.12.297-308Search in Google Scholar

[15] B. Ghanmi, N. H. Taieb and M. A. Hammami, Growth conditions for exponential stability of time-varying perturbed systems, Internat. J. Control 86 (2013), no. 6, 1086–1097. 10.1080/00207179.2013.774464Search in Google Scholar

[16] M. A. Hammami, On the stability of nonlinear control systems with uncertainty, J. Dynam. Control Systems 7 (2001), no. 2, 171–179. 10.1023/A:1013099004015Search in Google Scholar

[17] M. Hammi and M. A. Hammami, Gronwall–Bellman type integral inequalities and applications to global uniform asymptotic stability, Cubo 17 (2015), no. 3, 53–70. 10.4067/S0719-06462015000300004Search in Google Scholar

[18] M. Hammi and M. A. Hammami, Non-linear integral inequalities and applications to asymptotic stability, IMA J. Math. Control Inform. 32 (2015), no. 4, 717–735. 10.1093/imamci/dnu016Search in Google Scholar

[19] H. K. Khalil, Nonlinear Systems, 3rd ed., Prentice Hall, Upper Saddle River, 2002. Search in Google Scholar

[20] K. D. Kucche and P. U. Shikhare, Ulam stabilities for nonlinear Volterra delay integro-differential equations, J. Contemp. Math. Anal. 54 (2019), no. 5, 276–287. 10.3103/S1068362319050042Search in Google Scholar

[21] Y. Lin, E. D. Sontag and Y. Wang, A smooth converse Lyapunov theorem for robust stability, SIAM J. Control Optim. 34 (1996), no. 1, 124–160. 10.1137/S0363012993259981Search in Google Scholar

[22] M. Malisoff, Further results on Lyapunov functions and domains of attraction for perturbed asymptotically stable systems, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 12 (2005), no. 2, 193–225. Search in Google Scholar

[23] X. Mu and D. Cheng, On the stability and stabilization of time varying nonlinear control systems, Asian J. Control 7 (2005), no. 3, 244–255. 10.1111/j.1934-6093.2005.tb00234.xSearch in Google Scholar

[24] M. Vidyasagar, Nonlinear Systems Analysis, Classics Appl. Math. 42, Society for Industrial and Applied Mathematics, Philadelphia, 2002. 10.1137/1.9780898719185Search in Google Scholar

[25] L. Xiao, J. Bao and X. Shi, The global exponential stability analysis of nonlinear dynamic system and application, Appl. Comput. Math. 6 (2017), no. 2, 86–74. 10.11648/j.acm.20170602.11Search in Google Scholar

[26] B. Zheng, New generalized 2D nonlinear inequalities and applications in fractional differential-integral equations, J. Math. Inequal. 9 (2015), no. 1, 235–246. 10.7153/jmi-09-21Search in Google Scholar

[27] B. Zhou, On asymptotic stability of linear time-varying systems, Automatica J. IFAC 68 (2016), 266–276. 10.1016/j.automatica.2015.12.030Search in Google Scholar

[28] V. I. Zubov, Methods of A. M. Lyapunov and Their Application, P. Noordhoff, Groningen, 1964. Search in Google Scholar