Global exponential asymptotic stability in nonlinear discrete dynamical systems

Abstract

For the nonlinear discrete dynamical system xk+1=Txk on bounded, closed and convex set D⊂Rn, we present several sufficient and necessary conditions under which the unique equilibrium point is globally exponentially asymptotically stable. The infimum of exponential bounds of convergent trajectories is also derived. © 2001 Academic Press.

Author keywords Discrete dynamical systems; difference equations; global exponential asymptotic stability; exponential bound; topologically equivalent metric; contraction map