Some Recent Results for Continuous Switched Linear Systems

The elemental structure arising from the continuous autonomous switching of two linear systems is considered. After introducing certain canonical forms, some analytical results about limit cycle bifurcation are reported, showing that such systems generically exhibit a jump transition to oscillating behavior. Explicit expressions for quantitative characteristics of the periodic oscillation are obtained for the cases of dimension two and three. As another relevant result, it is shown that continuous n-dimensional switched linear systems whose both components are Hurwitz need not be globally asymptotically stable when n is greater or equal to 3.