I have not worked as much as I wanted on discrete-time systems.
Some results on discrete-time systems are given in the book:
I. Karafyllis and Z.-P. Jiang, Stability and Stabilization of Nonlinear Systems, Springer-Verlag, London (Series: Communications and Control Engineering), 2011.
Below is a list of papers that contain results on discrete-time systems.
I. Karafyllis, “Non-Uniform Robust Global Asymptotic Stability for Discrete-Time Systems and Applications to Numerical Analysis”, IMA Journal of Mathematical Control and Information, 23(1), 2006, pp. 11-41.
I. Karafyllis, “Non-Uniform in Time Robust Global Asymptotic Output Stability for Discrete-Time Systems”, International Journal of Robust and Nonlinear Control, 16(4), 2006, pp. 191-214.
I. Karafyllis and S. Kotsios, “Necessary and Sufficient Conditions for Robust Global Asymptotic Stabilization of Discrete-Time Systems”, Journal of Difference Equations and Applications, 12(7), 2006, pp. 741-768.
I. Karafyllis and C. Kravaris, “On the Observer Problem for Discrete-Time Control Systems”, IEEE Transactions on Automatic Control, 52(1), 2007, pp. 12-25.
G. Athanasiou, I. Karafyllis and S. Kotsios, “Price Stabilization Using Buffer Stocks”, Journal of Economic Dynamics and Control, 32(4), 2008, pp. 1212-1235.
I. Karafyllis and M. Krstic, “Robust Predictor Feedback for Discrete-Time Systems with Input Delays”, International Journal of Control, 86(9), 2013, pp. 1652-1663.
I. Karafyllis and M. Papageorgiou, “Global Exponential Stability for Discrete-Time Networks with Applications to Traffic Networks”, IEEE Transactions on Control of Network Systems, 2(1), 2015, pp. 68-77.
I. Karafyllis, M. Kontorinaki and M. Papageorgiou, “Global Exponential Stabilization of Freeway Models”, International Journal of Robust and Nonlinear Control, 26(6), 2016, pp. 1184-1210.
I. Karafyllis and M. Papageorgiou, “Stability Results for Simple Traffic Models Under PI-Regulator Control”, IMA Journal of Mathematical Control and Information, 33(2), 2016, pp. 209-229.
I. Karafyllis, M. Kontorinaki and M. Papageorgiou, “Robust Global Adaptive Exponential Stabilization of Discrete-Time Systems with Application to Freeway Traffic Control”, IEEE Transactions on Automatic Control, 62(12), 2017, pp. 6195-6208.
M. Kontorinaki, I. Karafyllis and M. Papageorgiou, “Global Exponential Stabilization of Acyclic Traffic Networks”, International Journal of Control, 92(3), 2019, pp. 564-584.