A sufficient condition for the existence of a common Lyapunov function for two second order linear systems

A sufficient condition for the existence of a common Lyapunov function for two stable linear second order systems x=A/sub i/x, A/sub i//spl isin/{A/sub l/, A/sub 2/} is presented, namely that the matrix pencil A/sub 1/+/spl gamma/A/sub 2/ have distinct negative eigenvalues for all /spl gamma//spl isin/(0,/spl infin/). The implications of this result for the stability of more general switching systems are briefly discussed.