Common diagonal Lyapunov function for third order linear switched system

Authors:
Taner Büyükköroğlu
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Cited 0

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Abstract

Consider the stability problem for the following linear switched system (differential inclusion) x@?=Ax,A@?{A"1,A"2,...,A"N}. Here A"i (i=1,2,...,N) are nxn dimensional Hurwitz stable real matrices. In this study for this system we investigate the problem of the existence and construction of a common diagonal Lyapunov function of the form V(x)=x^TDx where D is a positive diagonal matrix. In the case of n=3, i.e. third order system, we suggest a simple elimination algorithm which gives a common D in the case of existence.