Globally asymptotical stability for descriptor systems with nonlinear perturbations

The stability problems for descriptor systems with nonlinear perturbations have been widely considered. However, the existing results require the stability of the linear part of the system. This paper investigates globally asymptotical stability of descriptor systems with nonlinear perturbations, whose linear parts are allowed to be unstable. By using Lyapunov stability theory and linear matrix inequality (LMI), an LMI-based stability criterion is derived. Finally, an example is given to show the effectiveness of the proposed methods.