|
A sufficient condition for the existence of a Lyapunov function of the form V(x)=xTPx, P=PT>0, P ∈ IRnxn, for the stable linear time invariant systems x=Aix, Ai ∈ IRnxn, Ai ∈ A = {A1,...,Am},is that the matrices Ai are Hurwitz, and
that a non-singular matrix T exists, such that TAiT-1, i∈{1,...,m}is upper triangular (Mori, Mori & Kuroe 1996, Mori, Mori & Kuroe 1997, Liberzon, Hespanha & Morse 1998, Shorten & Narendra 1998). The existence of such a function referred to as a common quadratic Lyapunov function (CQLF), is sufficient to guarantee the exponential stability of the switching system x = A(t)x, A(t) ∈ A. In this paper we
investigate the stability properties of related classes of switching systems. We consider sets of matrices A, where no single matrix T exists that simultaneously transforms each
Ai ∈ A to upper triangular form, but where a set of non singular matrices Tij exist such that the matrices
{fTijAiT-1ij, TijAjT-1ij}, i,j ∈ {1,...,m}are upper tria...
|
