Stability in measure and asymptotic stability of uncertain nonlinear switched systems with a practical application

Abstract

In this paper, an uncertain nonlinear switched system is actually a nonlinear switched system disturbed by subjective uncertainties, usually written as several uncertain differential equations. Stability analysis of switched systems has been discussed in depth, while few results about stability of uncertain switched systems were published before. To fill this gap, stability in measure and asymptotic stability of uncertain nonlinear switched systems with countable switches in infinite-time horizon are both considered. The essential property of the solutions to such uncertain switched systems will be illustrated and captured from different perspectives with the help of the above stability analysis. Two theorems to judge these stabilities are proposed and then verified according to uncertainty theory and Lyapunov's second method. At last, a practical model of population growth is studied to display the validness of the results derived.