title: Robust observer-based absolute stabilization for Lur'e singularly perturbed systems with state delay.
abstract: This paper is concerned with the problem of robust observer-based absolute stabilization for Lur'e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods.
authors.affiliation: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China; Center for Applied and Multidisciplinary Mathematics, Department of Mathematics, East China Normal University, Shanghai 200241, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Liu
authors.affiliation: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China. Electronic address: yywang918@163.com.
authors.forename: Yanyan
authors.initials: Y
authors.lastname: Wang
keywords: Input-to-state stability (ISS); Linear matrix inequality (LMI); Lur’e singularly perturbed systems; Time-delay systems