Existence and uniqueness of solutions for uncertain nonlinear switched systems?

In this paper, an uncertain nonlinear switched system is a nonlinear switched system disturbed by subjective uncertainties, which can be formulated by several uncertain differential equations. Few results concerning such type of nonlinear switched systems were published before. To fill this gap, the property of solutions for uncertain nonlinear switched systems with finite-time horizon is discussed in depth. Based on two conditions called linear growth condition and Lipschitz condition, an existence and uniqueness theorem is proposed and demonstrated for the solutions of the uncertain nonlinear switched systems, and the main theoretical bases include uncertainty theory and Banach fixed point theorem. At last, a numerical example and a stock price model are given to illustrate the effectiveness of the results derived. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper discusses the properties of solutions for uncertain nonlinear switched systems with finite-time horizon and proposes an existence and uniqueness theorem. The research fills the gap in the study of such type of nonlinear switched systems.