References
- R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications, 2nd ed., Marcel Dekker, 2000.
- R. Baier, L. Grüne, and S. Hafstein, Linear programming based Lyapunov function computation for differential inclusions, Discrete Contin. Dyn. Syst. Ser. B 17(1) (2012), pp. 33–56. doi:10.3934/dcdsb.2012.17.33.
- H. Ban, and W.D. Kalies, A computational approach to Conley's decomposition theorem, J. Comput. Nonlinear Dyn. 1(4) (2006), pp. 312–319. doi:10.1115/1.2338651.
- J. Björnsson, P. Giesl, S. Hafstein, C.M. Kellett, and H. Li, Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction, Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, CA, USA, 2014, pp. 5506–5511.
- P. Giesl, On the determination of the basin of attraction of discrete dynamical systems, J. Differ. Equ. Appl. 13(6) (2007), pp. 523–546. doi:10.1080/10236190601135209.
- P. Giesl, Construction of a local and global Lyapunov function using radial basis functions, IMA J. Appl. Math 73(5) (2008), pp. 782–802. doi:10.1093/imamat/hxn018.
- P. Giesl, and S. Hafstein, Computation of Lyapunov functions for nonlinear discrete time systems by linear programming, J. Differ. Equ. Appl. 20(4) (2014), pp. 610–640. doi:10.1080/10236198.2013.867341.
- P. Giesl, and S. Hafstein, Revised CPA method to compute Lyapunov functions for nonlinear systems, J. Math. Anal. Appl. 410(1) (2014), pp. 292–306. doi:10.1016/j.jmaa.2013.08.014.
- S.P. Gordon, On converses to the stability theorems for difference equations, SIAM J. Control 10(1) (1972), pp. 76–81. doi:10.1137/0310007.
- S. Hafstein, C.M. Kellett, and H. Li, Continuous and piecewise affine Lyapunov functions using the Yoshizawa construction, Proceedings of 2014 American Control Conference, 2014, Portland, OR, USA, pp. 548–553, (no. 0158).
- S. Hafstein, C.M. Kellett, and H. Li, Computing continuous and piecewise affine Lyapunov functions for nonlinear systems, Submitted (June 2014)
- W. Hahn, Stability of Motion, Springer-Verlag, 1967.
- Z.-P. Jiang, and Y. Wang, A converse Lyapunov theorem for discrete-time systems with disturbances, Systems Control Lett. 45(1) (2002), pp. 49–58. doi:10.1016/S0167-6911(01)00164-5.
- W.D. Kalies, K. Mischaikow, and R.C.A.M. VanderVorst, An algorithmic approach to chain recurrence, Found. Comput. Math. 5(4) (2005), pp. 409–449. doi:10.1007/s10208-004-0163-9.
- C.M. Kellett, A compendium of comparison function results, Math. Control Signals Syst. 26(3) (2014), pp. 339–374. doi:10.1007/s00498-014-0128-8.
- C.M. Kellett, and A.R. Teel, Smooth Lyapunov functions and robustness of stability for difference inclusions, Systems Control Lett. 52(5) (2004), pp. 395–405. doi:10.1016/j.sysconle.2004.02.015.
- C.M. Kellett, and A.R. Teel, On the robustness of 𝒦ℒ-stability for difference inclusions: Smooth discrete-time Lyapunov functions, SIAM J. Control Optim. 44(3) (2005), pp. 777–800. doi:10.1137/S0363012903435862.
- S. Marinósson, Lyapunov function construction for ordinary differential equations with linear programming, Dyn. Syst. 17(2) (2002), pp. 137–150. doi:10.1080/0268111011011847.
- J.L. Massera, On Liapounoff's conditions of stability, Ann. Math. 50(3) (1949), pp. 705–721. doi:10.2307/1969558.
- E.D. Sontag, Comments on integral variants of ISS, Systems Control Lett. 34(1–2) (1998), pp. 93–100. doi:10.1016/S0167-6911(98)00003-6.
- A. Stuart, and A. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge, UK, 1996.
- T. Yoshizawa, On the stability of solutions of a system of differential equations, Mem. Coll. Sci. Univ. Kyoto, Ser. A Math. 29 (1955), pp. 27–33.
- T. Yoshizawa, Stability theory by Liapunov's second method, The Mathematical Society of Japan, Tokyo, 1966.