Lecture Notes in Control and Information Sciences

Stability Analysis and Design for Nonlinear Singular Systems

Authors: Yang, Chunyu, Zhang, Qingling, Zhou, Linna

  • Recent research on practical stability of nonlinear singular systems
  • Provides global stability analysis and design methods for nonlinear singular systems
  • Written by leading experts in the field
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About this book

Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc.

Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability for standard state-space systems were generalized to singular systems. For Lur’e type descriptor systems (LDS) which were the feedback interconnection of a descriptor system with a static nonlinearity, strongly absolute stability was defined and Circle criterion and Popov criterion were derived. The notion of input-state stability (ISS) for nonlinear singular systems was defined based on the concept of ISS for standard state-space systems and the characteristics of singular systems. LMI-based sufficient conditions for ISS of Lur’e singular systems were proposed. Furthermore, observer design for nonlinear singular systems was studied and some observer design methods were proposed by the obtained stability results and convex optimization algorithms. Finally, absolute stability and multi-objective control of nonlinear singularly perturbed systems were considered. By Lyapunov functions, absolute stability criteria of Lur’e singularly perturbed systems were proposed and multi-objective control of T-S fuzzy singularly perturbed systems was achieved. Compared with the existing results, the obtained methods do not depend on the decomposition of the original system and can produce a determinate upper bound for the singular perturbation parameter.

 

Table of contents (7 chapters)

  • Introduction

    Yang, Chunyu (et al.)

    Pages 1-11

  • Practical Stability Analysis and Synthesis for Nonlinear Singular Systems

    Yang, Chunyu (et al.)

    Pages 13-47

  • Strongly Absolute Stability Analysis for Lur’e Singular Systems

    Yang, Chunyu (et al.)

    Pages 49-99

  • Input-to-State Stability Analysis and Design for Lur’e Singular Systems

    Yang, Chunyu (et al.)

    Pages 101-123

  • Observer Design for Nonlinear Singular Systems

    Yang, Chunyu (et al.)

    Pages 125-153

Buy this book

eBook $79.95
price for USA (gross)
  • ISBN 978-3-642-32144-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA
  • ISBN 978-3-642-32143-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Stability Analysis and Design for Nonlinear Singular Systems
Authors
Series Title
Lecture Notes in Control and Information Sciences
Series Volume
435
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-32144-3
DOI
10.1007/978-3-642-32144-3
Softcover ISBN
978-3-642-32143-6
Series ISSN
0170-8643
Edition Number
1
Number of Pages
XII, 212
Number of Illustrations and Tables
32 b/w illustrations
Topics