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      SOS methods for stability analysis of neutral differential systems

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      Author
      Peet, M. M.
      Bonnet, C.
      Özbay, Hitay
      Date
      2009
      Source Title
      Lecture Notes in Control and Information Sciences
      Print ISSN
      0170-8643
      Publisher
      Springer
      Volume
      388
      Pages
      97 - 107
      Language
      English
      Type
      Conference Paper
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      Abstract
      This paper gives a description of how "sum-of-squares" (SOS) techniques can be used to check frequency-domain conditions for the stability of neutral differential systems. For delay-dependent stability, we adapt an approach of Zhang et al. [10] and show how the associated conditions can be expressed as the infeasibility of certain semialgebraic sets. For delay-independent stability, we propose an alternative method of reducing the problem to infeasibility of certain semialgebraic sets. Then, using Positivstellensatz results from semi-algebraic geometry, we convert these infeasibility conditions to feasibility problems using sum-of-squares variables. By bounding the degree of the variables and using the Matlab toolbox SOSTOOLS [7], these conditions can be checked using semidefinite programming.
      Keywords
      Alternative methods
      Delay independent
      Delay-dependent stability
      Feasibility problem
      Frequency domains
      Matlab toolboxes
      Neutral differential systems
      Permalink
      http://hdl.handle.net/11693/28734
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/978-3-642-02897-7_9
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      • Department of Electrical and Electronics Engineering 3619
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