DocumentCode :
2162042
Title :
A Lie-algebraic analysis of the problem of absolute stability
Author :
Margaliot, Michael ; Yfoulis, Christos
Author_Institution :
Sch. of Electr. Eng. Syst., Tel Aviv Univ., Tel Aviv, Israel
fYear :
2007
fDate :
2-5 July 2007
Firstpage :
680
Lastpage :
687
Abstract :
The absolute stability problem (ASP) entails determining a critical parameter value for which a feedback system, composed of an nth-order linear system and a sector-bounded nonlinear function, loses its stability. The ASP is one of the oldest open problems in the theory of stability and control. Recently, it is attracting considerable interest, as solving it is equivalent to providing a necessary and sufficient condition for the stability of linear switched systems under arbitrary switching. Pyatnitsky pioneered the most promising approach for addressing the ASP. His approach is based on using optimal control techniques for characterizing the “most destabilizing” sector-bounded nonlinear function. This is equivalent to characterizing the “most destabilizing” switching law for a linear switched system under arbitrary switching. In this paper, we develop a new approach to the ASP which is based on a Lie-algebraic analysis of the switching function that determines the optimal control. We show that the finiteness of the associated Lie algebra implies that the switching function itself is the solution of a switched linear system of order at most n2. Furthermore, the switching function has a special and symmetric structure. This makes it possible to obtain an explicit analytic expression for the switching function for low orders of n. We demonstrate this using two examples.
Keywords :
Lie algebras; absolute stability; feedback; linear systems; optimal control; switching systems (control); ASP; Lie-algebraic analysis; absolute stability problem; feedback system; linear switched system stability; nonlinear function; nth-order linear system; optimal control technique; Linear systems; Optimal control; Stability criteria; Switched systems; Switches; Trajectory;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control Conference (ECC), 2007 European
Conference_Location :
Kos
Print_ISBN :
978-3-9524173-8-6
Type :
conf
Filename :
7068591
Link To Document :
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