Nonlinear interconnected systems described by integro-differential equations

In this paper, a class of multi-input and multi-output nonlinear systems described by integro-differential equations are studied. Some frequency domain conditions are established for estimation of the period and frequency of periodic solutions of the second kind which is a close cycle in cylindrical phase space for a class input-output interconnected pendulum-like systems. The effects of interconnections are shown through a permutation matrix, and then upper bounds for the frequency of periodic solutions of the second kind can be presented. Numerical examples are given to illustrate the main results of the paper. Examples show that input and output interchange presented here can result in some great changes in some practical systems. Chaotic phenomenon appears in partial variables of pendulum-like systems in Example 1.