Absolute Stability of Lur’e Singularly Perturbed Systems

Abstract

In this chapter, absolute stability of Lur’e singularly perturbed systems is studied. First, we propose two lemmas which are the theory basis for constructing ε-dependent Lyapunov functions. Then, circle criterion and Popov criterion for absolute stability of Lur’e singularly perturbed systems are derived by using ε-dependent quadratic Lyapunov function and Lur’e Lyapunov function, respectively. Based on the stability criterion, an algorithm is proposed to compute the stability bound that is shown to be less conservative than those computed using other existing methods. Compared with the existing results, the obtained methods do not depend on the decomposition of the original system and can produce an determinate upper bound for the singular perturbation parameter.