Criteria for the absence of limit cycles in two-dimensional discrete systems

Sufficient conditions for the nonexistence of zero input limit cycles in two-dimensional systems which contain a finite number of memoryless nonlinearities are presented. Two different conditions are given. The first one is based on the frequency domain representation of the linear part of the discrete system, and it is shown to be more general than the one already presented in [1]. The second condition is formulated using the state space representation and is based on the properties of quasidominant matrices and on partial results on the 2-D Lyapunov equation.