On the Stability of Discrete Systems

R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.MATHGoogle Scholar

S. Elaydi, An Introduction to Difference Equations, 2nd ed., Springer-Verlag, New York, 1999.MATHGoogle Scholar

I.V. Gaishun, Systems with Discrete Time, Institute of Mathematics of Belarus, Minsk, 2001 (Russian).Google Scholar

V. Lakshmikantham and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications, Academic Press, New York-London, 1998.Google Scholar

R.I. Gladilina and A.O. Ignatyev, On necessary and sufficient conditions for the asymptotic stability of impulsive systems, Ukrain. Math. J. 55 (2003), 1254–1264.MATHCrossRefGoogle Scholar

A. Halanay and D. Wexler, Qualitative Theory of Impulsive Systems, Mir, Moscow, 1971 (Russian).Google Scholar

A.O. Ignatyev, Method of Lyapunov functions in problems of stability of solutions of systems of differential equations with impulse action, Sb. Mat. 194 (2003), 1543–1558.CrossRefGoogle Scholar

V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov, Theory of Impulsive Differential Equations, Wiley, Singapore-London, 1989.MATHGoogle Scholar

A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.MATHGoogle Scholar

R. Abu-Saris, S. Elaydi, and S. Jang, Poincaré type solutions of systems of difference equations, J. Math. Anal. Appl. 275 (2002), 69–83.MATHMathSciNetCrossRefGoogle Scholar

R.P. Agarwal, W.-T. Li, and P.Y.H. Pang, Asymptotic behavior of nonlinear difference systems, Appl. Math. Comput. 140 (2003), 307–316.MATHMathSciNetCrossRefGoogle Scholar

C. Corduneanu, Discrete qualitative inequalities and applications, Nonlinear Anal. TMA 25 (1995), 933–939.MATHMathSciNetCrossRefGoogle Scholar

I. Győri, G. Ladas, and P.N. Vlahos, Global attractivity in a delay difference equation, Nonlinear Anal. TMA 17 (1991), 473–479.CrossRefGoogle Scholar

I. Győri and M. Pituk, The converse of the theorem on stability by the first approximation for difference equations, Nonlinear Anal. 47 (2001), 4635–4640.MathSciNetCrossRefGoogle Scholar

J.W. Hooker, M.K. Kwong, and W.T. Patula, Oscillatory second order linear difference equations and Riccati equations, SIAM J. Math. Anal. 18 (1987), 54–63.MATHMathSciNetCrossRefGoogle Scholar

P. Marzulli and D. Trigiante, Stability and convergence of boundary value methods for solving ODE, J. Difference Equations Appl. 1 (1995), 45–55.MATHMathSciNetGoogle Scholar

A. Bacciotti and A. Biglio, Some remarks about stability of nonlinear discrete-time control systems, Nonlinear Differential Equations Appl. 8 (2001), 425–438.MATHMathSciNetCrossRefGoogle Scholar

A.O. Ignatyev, Stability of the zero solution of an almost periodic system of finite-difference equations, Differential Equations 40 (2004), 105–110.MathSciNetCrossRefGoogle Scholar

R. Bouyekhf and L.T. Gruyitch, Novel development of the Lyapunov stability theory for discrete-time systems, Nonlinear Anal. 42 (2000), 463–485.MATHMathSciNetCrossRefGoogle Scholar

W. Hahn, Stability of Motion, Springer-Verlag, Berlin-Heidelberg-New York, 1967.MATHGoogle Scholar

N. Rouche, P. Habets, and M. Laloy, Stability Theory by Liapunov’s Direct Method, Springer-Verlag, New York, 1977.Google Scholar

A.Ya. Savchenko and A.O. Ignatyev, Some Problems of the Stability Theory, Naukova Dumka, Kiev, 1989 (Russian).Google Scholar

C. Corduneanu, Almost Periodic Functions, 2nd ed., Chelsea, New York, 1989.MATHGoogle Scholar