Novel development of the Lyapunov stability theory for discrete-time systems. II: Stability criteria (Q1582119)

The authors develop a theory of Lyapunov stability for discrete-time nonlinear systems \[ x(t_{k+1})= f(t_k, x(t_k)). \] They are mainly concerned with the dependence of several stability concepts on the initial time (uniform and nonuniform stability). In this paper, they give necessary conditions and, separately, sufficient conditions for asymptotic stability. They also give sufficient conditions for nonuniform asymptotic stability, and sufficient conditions for uniform asymptotic stability (with exact determination of the stability domain).