Summary
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
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© 2009 Springer-Verlag Berlin Heidelberg
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Peet, M.M., Bonnet, C., Özbay, H. (2009). SOS Methods for Stability Analysis of Neutral Differential Systems. In: Loiseau, J.J., Michiels, W., Niculescu, SI., Sipahi, R. (eds) Topics in Time Delay Systems. Lecture Notes in Control and Information Sciences, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02897-7_9
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DOI: https://doi.org/10.1007/978-3-642-02897-7_9
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