Stability and stabilization for generalized quasi‐one‐sided Lipschitz nonlinear neutral systems with multiple delays

Abstract In this article, a generalized weak quasi‐one‐sided Lipschitz condition is firstly introduced to study the problem of stability and stabilization for a class of nonlinear neutral systems with multiple delays. Under the generalized weak quasi‐one‐sided Lipschitz condition, the asymptotic stability criterion for nonlinear neutral systems with multiple delays holds, even though the parameter matrix of nonlinear neutral systems is unstable. Meanwhile, the sufficient condition for the asymptotic stability of the zero solution of nonlinear neutral closed‐loop systems holds, even if the system's parameter is not stabilizable. It has been proven that the generalized weak quasi‐one‐sided Lipschitz condition is superior to the Lipschitz condition in achieving stability and stabilization for nonlinear neutral systems with multiple delays. Finally, the effectiveness of the obtained results is verified through a simulation example.