Abstract
Sufficient conditions are presented for the boundedness of the solutions of a vector nonlinear Volterra integral equation of the second kind that frequently arises in the study of automatic control systems containing an arbitrary finite number of time-varying nonlinear elements. Similar conditions are given for the boundedness of the solutions of the discrete analog of the integral equation. A direct application of the results yields a Nyquist-like frequency-domain condition for the “bounded-input implies bounded-output stability” of a large class of feedback systems containing a single time-varying nonlinear element.
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