A novel ε-dependent Lyapunov function and its application to singularly perturbed systems

The ε-dependent Lyapunov method is an effective technique to analyze both standard and nonstandard singularly perturbed systems, and the constructed ε-dependent Lyapunov function has an impact on the conservatism of the obtained results. This paper proposes a novel ε-dependent Lyapunov function, which includes three classes of common ε-dependent Lyapunov functions in the existing literature and can lead to less conservative results. Firstly, the novel ε-dependent Lyapunov function is introduced, and then it is used to analyze the stability and dissipativity of singularly perturbed Lur'e systems. Some stability and dissipativity analysis criteria are obtained for the singularly perturbed Lur'e systems by using the novel ε-dependent Lyapunov function. The superiority of the obtained analysis criteria is shown by an illustrative example.