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

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.