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On the simultaneous diagonal stability of a pair of positive linear systems. (English) Zbl 1094.93021
The authors consider a pair of positive linear time-invariant systems x ˙=A i x, i=1,2, i.e. A 1 ,A 2 are Metzler matrices. They study conditions for which both systems have a diagonal common quadratic Lyapunov function (CQLF). Their main result is that under the assumption that A 1 and A 2 are Hurwitz and have no zero entries the existence of a diagonal CQLF is equivalent to the condition that A 1 +DA 2 D is non-singular for all positiv definite diagonal matrices D. The paper is well structured and nicely written.
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