Design of controller for Lur’e systems guaranteeing dichotomy

摘要

In this paper, the problem of controller design for Lur’e systems guaranteeing dichotomy is investigated. On the basis of Kalman–Yakubovich–Popov (KYP) lemma and two frequency equalities, a new methodology for the dichotomy analysis of the Lur’e systems is proposed. A linear matrix inequality (LMI) based criterion is derived, which is equivalent to the Leonov’s frequency-domain one, while for the dichotomy analysis and synthesis which is more straightforward than the frequency-domain one. In virtue of this result, a dynamic output feedback controller ensuring the dichotomy property for Lur’e systems is designed. Finally a numerical example is included to demonstrate the validity and the applicability of the proposed approach.