Absolute stability of Lur'e singularly perturbed systems with multiple nonlinearities

摘要

This paper investigates the absolute stability problem for Lur''e singularly perturbed systems with multiple nonlinearities. The objective is to determine if the system is absolutely stable for any ε ∈ (0, ε0], where ε denotes the perturbation parameter and ε0 is a pre-defined positive scalar. Firstly, an ε-dependent Lyapunov function of Lur''e-postnikov form is constructed. Then, a stability criterion expressed in terms of ε-independent linear matrix inequalities (LMIs) is derived. Finally, an example is given to show the feasibility and effectiveness of the obtained method.