On practical stability.

Abstract

In this paper, a class of nonlinear nonautonomous systems with multiple nonlinearities is considered. Sufficient conditions are developed for a type of practical stability with specified settling time. The conditions are independent of the actual form of nonlinear characteristics so that they can be interpreted as conditions for 'absolute' practical stability. The stability test is reduced to verification of the Hurwitz property of a constant matrix. This makes the stability analysis of the considered class of nonlinear systems convenient for machine computations. The proposed practical stability analysis is applied to a third-order system with several nonlinearities.