Popov absolute stability criterion for time-varying multivariable nonlinear systems

Abstract

This paper extends in a simple way the classical absolute stability Popov criterion to multivariable rational systems with time-varying memoryless nonlinearities subject to sea or conditions. The proposed sufficient conditions are expressed in terms of easy-to-check Linear Matrix Inequalities, or under frequency-domain form well-suited for robustness issues, and lead to simple graphical interpretations. Apart from the usual conditions, the results assume basically a sector condition on the derivative of the nonlinearities with respect to time. Results for local and global stability are given.