Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423004 | Journal of Computational and Applied Mathematics | 2012 | 7 Pages |
Consider the stability problem for the following linear switched system (differential inclusion) xÌ=Ax,Aâ{A1,A2,â¦,AN}. Here Ai (i=1,2,â¦,N) are nÃn 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)=xTDx 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.
⺠We consider n-dimensional linear switched systems. ⺠Construction of a common diagonal Lyapunov function for the systems is considered. ⺠A simple elimination algorithm for third order system is given. ⺠For the general case, we apply Kelly's cutting-plane method to the given problem.