Stability of switched systems: a Lie-algebraic condition

We present a sufficient condition for asymptotic stability of a switched li near system in terms of the Lie algebra generated by the individual matrice s. Namely, if this Lie algebra is solvable, then the switched system is exp onentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common L yapunov function. We also discuss the implications of this result for switc hed nonlinear systems. (C) 1999 Elsevier Science B.V. All rights reserved.