Zero-state observability and stability of discrete-time nonlinear systems
The paper studies discrete-time, stationary, finite-dimensional nonlinear dynamical systems. It is shown how asymptotic stability can be determined by zero-state observability and square summability of the observable functions. Moreover, the relationships between Lyapunov stability and asymptotic stability are studied. Finally, the feedback stabilization problem is also considered and relations to existing results are discussed. The paper contains several remarks and comments on observability and stability results for nonlinear discrete-time dynamical systems. Similar problems have been recently considered in the paper [\textit{A. S. Morse}, IEEE Trans. Autom. Control 35, 1002-1012 (1990; Zbl 0724.93047)].
scientific article; zbMATH DE number 758492