Combination of invariant sets as a tool for stabilization

The stability and stabilization of a class of linear time-varying systems is studied. The class of systems considered is a linear time-varying combination of linear time-invariant systems. Two classes of time varying combinations are considered: a `persistently exciting´ one and switched one. The concept of de-multiplexed controls is also introduced in relation to the switching case. Ideas from invariant sets and Lyapunov theory are used for the analysis while the results are given in terms of linear matrix inequalities