Exponential stability of discrete-time systems, stability domains, and state bounds are obtained with the use of vector norm Lyapunov functions. For linear systems, necessary and sufficient conditions are given for asymptotic stability, and exponential bounds are derived. For nonlinear systems, sufficient conditions for exponential stability also yield a stability domain and exponential bounds. Applications are demonstrated in observer design for uncertain discrete-time nonlinear systems.

Proceedings of the 1994 American Control Conference. Part 1 (of 3)
Department of Systems and Computer Engineering

Aitken, V, & Schwartz, H.M. (1994). On the exponential stability of discrete-time systems with applications in observer design. In Proceedings of the American Control Conference (pp. 2196–2201).