Frequency domain criteria for the absence of zero-input limit cycles in nonlinear discrete-time systems, with applications to digital filters
T. Claasen, W. Mecklenbräuker, Joshua Peek · IEEE Transactions on Circuits and Systems · 1975
On the basis of a theorem of Barkin, a number of criteria are derived which give sufficient conditions for the absence of zero-input limit cycles in discrete-time and especially digital systems. These criteria are formulated in the frequency domain and provide a possibility of investigating the absence of a zero-input limit cycle of a specific lengthN. Depending on the particular characteristics of the nonlinearities and the number of nonlinearities in the system, different criteria are obtained. Application of the criteria results in most cases in a linear programming problem. The solutions to this problem for the case of a second-order digital filter with one and with two quantization nonlinearities are discussed.