Positivity of Complete Quadratic Lyapunov-Krasovskii Functionals in Time-Delay Systems

Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 423)

Abstract

This chapter discusses positivity of quadratic functionals that arise in the stability analysis of time-delay systems. When both the single and double integral terms are positive, a necessary and sufficient condition for positivity is obtained using operator theory. This is applied to the Lyapunov-Krasovskii functional and its derivative. The coupled differential-difference equations are studied using the Sum-of-Squares (SOS) method.

Keywords

Polynomial Matrice Quadratic Inequality Quadratic Functional Small State Space Continuous Matrix Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringSouthern Illinois University EdwardsvilleEdwardsvilleUSA
  2. 2.School of AutomationNanjing University of Science and TechnologyNanjingChina
  3. 3.Department of Mechanical, Materials, and Aerospace EngineeringIllinois Institute of TechnologyChicagoUSA

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