TY - JOUR
T1 - Absolute stability of third-order systems
T2 - A numerical algorithm
AU - Margaliot, Michael
AU - Yfoulis, Christos
N1 - Funding Information:
This research was supported in part by the ISF under Grant number 199/03. An abridged version of this paper was presented at the 44th IEEE Conference on Decision and Control. This paper was recommended for publication in revised form by Associate Editor Minyue Fu under the direction of Editor Roberto Tempo.
PY - 2006/10
Y1 - 2006/10
N2 - The problem of absolute stability is one of the oldest open problems in the theory of control. Even for the particular case of second-order systems a complete solution was presented only very recently. For third-order systems, the most general theoretical results were obtained by Barabanov. He derived an implicit characterization of the "most destabilizing" nonlinearity using a variational approach. In this paper, we show that his approach yields a simple and efficient numerical scheme for solving the problem in the case of third-order systems. This allows the determination of the critical value where stability is lost in a tractable and accurate fashion. This value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem.
AB - The problem of absolute stability is one of the oldest open problems in the theory of control. Even for the particular case of second-order systems a complete solution was presented only very recently. For third-order systems, the most general theoretical results were obtained by Barabanov. He derived an implicit characterization of the "most destabilizing" nonlinearity using a variational approach. In this paper, we show that his approach yields a simple and efficient numerical scheme for solving the problem in the case of third-order systems. This allows the determination of the critical value where stability is lost in a tractable and accurate fashion. This value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem.
KW - Differential inclusions
KW - Optimal control
KW - Stability under arbitrary switching
KW - Switched linear systems
UR - http://www.scopus.com/inward/record.url?scp=33747780415&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2006.04.025
DO - 10.1016/j.automatica.2006.04.025
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AN - SCOPUS:33747780415
SN - 0005-1098
VL - 42
SP - 1705
EP - 1711
JO - Automatica
JF - Automatica
IS - 10
ER -