Analysis of stability nonlinear systems with varying parameters using Popov criterion

This paper establishes sufficient conditions for absolute stability of time-varying control systems. The proposed conditions extend in a simple way the classical Popov criterion to time-varying memoryless nonlinearities, using previous results of Kharitonov. They are expressed in terms of linear matrix inequalities (LMIs). A weaker frequency domain criterion is deduced, leading to a simple graphical interpretation. The results ensure in general local stability, however, the stability is global for linear time-varying systems. Examples are presented to show the efficacy of these extensions within the MATLAB environment