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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 $\dot{x} = A_i x$, $i=1,2$, 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 $A_1+D A_2 D$ is non-singular for all positiv definite diagonal matrices $D$. The paper is well structured and nicely written.

93D30Scalar and vector Lyapunov functions
93D05Lyapunov and other classical stabilities of control systems
34D20Stability of ODE
Full Text: DOI
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