Extended-Routh´s approach for the stability analysis of nonlinear discrete time systems

In this paper, we present an innovative approach for stability analysis of nonlinear discrete time-varying systems introducing a new notion of dynamic poles and Extended-Routh´s stability approach. The stability analysis is carried out by introducing a new notion of dynamic characteristic equation for the nonlinear discrete time-varying system and defining the dynamic poles in m-plane. The m-plane for nonlinear time varying discrete systems is similar to that of the z-plane for linear time invariant discrete systems. The stability theorem is established and applied to various classes of nonlinear discrete systems.