Improved stability criteria for linear time-varying systems on time scales

References

• Aeyels, D., & Peuteman, J. (1998). A new asymptotic stability criterion for nonlinear time-variant differential equations. IEEE Transactions on Automatic Control, 43(7), 968–971. doi: 10.1109/9.701102
   Web of Science ®Google Scholar
• Aeyels, D., & Peuteman, J. (1999). Uniform asymptotic stability of linear time-varying systems. In V. Blondel and A. Megretski (Eds), Open problems in mathematical systems and control theory. London, UK: Springer-Verlag.
   Google Scholar
• Agarwal, R. P. (2000). Difference equations and inequalities: Theory, methods, and applications.Boca Raton, FL: CRC Press.
   Google Scholar
• András, S., & Mészáros, A. R. (2013). Ulam–Hyers stability of dynamic equations on time scales via Picard operators. Applied Mathematics and Computation, 219(9), 4853–4864. doi: 10.1016/j.amc.2012.10.115
   Web of Science ®Google Scholar
• Bartosiewicz, Z. (2016). Invariance and monotonicity of nonlinear systems on time scales. Systems and Control Letters, 93, 58–63. doi: 10.1016/j.sysconle.2016.04.001
   Web of Science ®Google Scholar
• Bartosiewicz, Z., & Piotrowska, E. (2013). On stabilisability of nonlinear systems on time scales. International Journal of Control, 86(1), 139–145. doi: 10.1080/00207179.2012.721563
   Web of Science ®Google Scholar
• Bellman, R. (1953). Stability theory of differential equations. New York: McGraw-Hill.
   Google Scholar
• Bohner, M., & Georgiev, S. G. (2016). Multivariable dynamic calculus on time scales. Berlin, Heidelberg: Springer-Verlag.
   Google Scholar
• Bohner, M., & Peterson, A. (2001). Dynamic equations on time scales-an introduction with applications. Boston: Birkhauser.
   Google Scholar
• Carmichael, R. D. (1912). The general theory of linear q-difference equations. American Journal of Mathematics, 34(2), 147–168. doi: 10.2307/2369887
   Google Scholar
• Da Cunha, J. J. (2005). Stability for time varying linear dynamic systems on time scales. Journal of Computational and Applied Mathematics, 176(2), 381–410. doi: 10.1016/j.cam.2004.07.026
   Web of Science ®Google Scholar
• Doan, T. S., Kalauch, A., Siegmund, S., & Wirth, F. R. (2010). Stability radii for positive linear time-invariant systems on time scales. Systems and Control Letters, 59(3), 173–179. doi: 10.1016/j.sysconle.2010.01.002
   Web of Science ®Google Scholar
• Du, N. H. (2007). On the exponential stability of dynamic equations on time scales. Journal of Mathematical Analysis and Applications, 331(2), 1159–1174. doi: 10.1016/j.jmaa.2006.09.033
   Web of Science ®Google Scholar
• Du, N. H., & Liem, N. C. (2011). Stability radius of implicit dynamic equations with constant coefficients on time scales. Systems and Control Letters, 60(8), 596–603. doi: 10.1016/j.sysconle.2011.04.018
   Web of Science ®Google Scholar
• Harris, C. J., Miles, J. F. (1980). Stability of linear systems: some aspects of kinematic similarity. London: Academic Press.
   Google Scholar
• Jackson, F. H. (1910). q-Difference equations. American Journal of Mathematics, 32(4), 305–314. doi: 10.2307/2370183
   Google Scholar
• Jungers, R. M., Ahmadi, A. A., Parrilo, P. A., & Mardavij, R. (2017). A characterization of Lyapunov inequalities for stability of switched systems. IEEE Transactions on Automatic Control, 62(6), 3062–3067. doi: 10.1109/TAC.2017.2671345
   Web of Science ®Google Scholar
• Kalman, R. E., & Bertram, J. E. (1960). Control system analysis and design via the ‘second method’ of Lyapunov, II discrete-time systems. Journal of Basic Engineering, 82, 394–400. doi: 10.1115/1.3662605
   Google Scholar
• Khalil, H. K. (2002). Nonlinear systems. Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Li, X., & Wu, J. (2016). Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica, 64, 63–69. doi: 10.1016/j.automatica.2015.10.002
   Web of Science ®Google Scholar
• Li, X., Zhang, X., & Song, S. (2017). Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica, 76, 378–382. doi: 10.1016/j.automatica.2016.08.009
   Web of Science ®Google Scholar
• Lu, X., Wang, Y., & Zhao, Y. (2016). Synchronization of complex dynamical networks on time scales via Wirtinger-based inequality. Neurocomputing, 216, 143–149. doi: 10.1016/j.neucom.2016.07.031
   Web of Science ®Google Scholar
• Lu, X., Zhang, X., & Liu, Q. (2018). Finite-time synchronization of nonlinear complex dynamical networks on time scales via pinning impulsive control. Neurocomputing, 275, 2104–2110. doi: 10.1016/j.neucom.2017.10.033
   Web of Science ®Google Scholar
• Martynyuk, A. (2016). Stability theory for dynamic equations on time scales. Basel, Switzerland: Springer International Publishing.
   Google Scholar
• Rugh, W. J. (1996). Linear system theory. 2nd ed. Upper Saddle River, NJ: Prentice Hall.
   Google Scholar
• Szyda, A. (2010). Stability of time-varying linear system. Pomiary, Automatyka, Kontrola, 56, 1364–1367.
   Web of Science ®Google Scholar
• Zafer, A. (2013). The stability of linear periodic Hamiltonian systems on time scales. Applied Mathematics Letters, 26(3), 330–336. doi: 10.1016/j.aml.2012.09.014
   Web of Science ®Google Scholar
• Zhou, B. (2016). On asymptotic stability of linear time-varying systems. Automatica, 68, 266–276. doi: 10.1016/j.automatica.2015.12.030
   Web of Science ®Google Scholar
• Zhou, B., & Zhao, T. (2017). On asymptotic stability of discrete-time linear time-varying systems. IEEE Transactions on Automatic Control, 62(8), 4274–4281. doi: 10.1109/TAC.2017.2689499
   Web of Science ®Google Scholar