A solution to the common Lyapunov function problem for continuous-time systems

The common Lyapunov function problem studied here is to find a set of linear systems, which has a common quadratic Lyapunov function V(x)=x ^TPx. This problem comes from the stability analysis of diverse fields of control systems. We present new sets of linear continuous-time constant systems having a common quadratic Lyapunov function. The classes obtained consist of systems whose system matrices are transformed into complex triangular matrices by a common complex matrix, or are close to them. We also show that the obtained classes include those presented by Narendra et al. (1994) and Mori et al. (1996)