TY - GEN
T1 - SOS methods for stability analysis of neutral differential Ssystems
AU - Peet, Matthew M.
AU - Bonnet, Catherine
AU - Özbay, Hitay
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70349931304&partnerID=8YFLogxK
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U2 - 10.1007/978-3-642-02897-7_9
DO - 10.1007/978-3-642-02897-7_9
M3 - Conference contribution
AN - SCOPUS:70349931304
SN - 9783642028960
T3 - Lecture Notes in Control and Information Sciences
SP - 97
EP - 107
BT - Topics in Time Delay Systems
A2 - Loiseau, Jean Jacques
A2 - Michiels, Wim
A2 - Niculescu, Silviu-Iulian
A2 - Sipahi, Rifat
ER -