A state-dependent switching law to quadratically stabilise switched linear systems

This paper generalises a Lyapunov based control strategy, developed in [4], which stabilises a switched linear system consisting of a pair of sub-systems, to a system consisting of arbitrarily many sub-systems. It is shown that the existence of a stable convex combination of the system matrices is a sufficient condition for the proposed control law to stabilise the switched system. Three examples are given of the proposed control law stabilising a system.