Exponential stabilizability and robustness analysis for discrete-time nonlinear systems. (English) Zbl 1122.93054

Summary: We derive some results on the exponential stabilizability and robustness analysis for discrete-time nonlinear control systems. Using the discrete Gronwall’s inequality, we also derive an important absolute estimate for the robustness index of the controlled discrete-time nonlinear system.


93C55 Discrete-time control/observation systems
93D09 Robust stability
93D15 Stabilization of systems by feedback
93D21 Adaptive or robust stabilization
Full Text: DOI


[1] Zabczyk, J., Some comments on stabilizability, Appl. math. optim., 19, 1-9, (1988) · Zbl 0654.93054
[2] Zabczyk, J., Mathematical theory: an introduction, (1992), Birkhäuser Boston · Zbl 1071.93500
[3] Hahn, W., On the application of the method of Lyapunov to difference equations, Math. ann., 136, 403-441, (1958)
[4] LaSalle, J.P., The stability and control of discrete processes, (1986), Springer New York · Zbl 0606.93001
[5] Agarwal, R.P., Difference equations and inequalities, (1992), Marcel Dekker New York · Zbl 0784.33008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.