Strongly Absolute Stability Analysis for Lur’e Singular Systems

Abstract

Absolute stability of Lur’e system whose forward path is a linear timeinvariant system and the feedback path is a nonlinearity satisfying sector constraints is one of the basic problems in control theory. In this chapter, strongly absolute stability of Lur’e singular systems is studied. Circle criterion and Popov criterion are derived. First, the concept of strongly absolute stability of Lur’e singular systems is defined and the positive realness of singular systems is discussed. Second, single-input-single-output Lur’e singular systems are considered and the graphical representation of circle criterion is given. Third, multiple-input-multiple-output Lur’e singular systems are considered and an LMI-based circle criterion is derived by a generalized Lyaponov function and S-procedure. Then, Popov criterion for standard state-space systems is generalized to singular systems. Finally, we propose a generalized Lur’e Lyaponov function (GLLF), by which a Popov-like criterion is derived.