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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Yang, C., Zhang, Q., Zhou, L. (2013). Strongly Absolute Stability Analysis for Lur’e Singular Systems. In: Stability Analysis and Design for Nonlinear Singular Systems. Lecture Notes in Control and Information Sciences, vol 435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32144-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-32144-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32143-6
Online ISBN: 978-3-642-32144-3
eBook Packages: EngineeringEngineering (R0)