On the existence of periodic behaviour of switched linear systems
A generalised implicit function theorem is used to show the existence of periodic solutions of switched linear systems with inhomogeneous terms (a subclass of hybrid systems) around an operating (compare: equilibrium) point. If the period concerned is small, the solutions 'move around' such an operating point. These points cannot generally be achieved by the individual linear systems. A central question to be answered is: which operating points are possible? Another question answered is what the asymptotic behaviour of the solutions near such an operating point look like (as a function of the period). For some specific cases, for instance when the systems only differ in the inhomogeneous terms, special results are obtained. The implicit function theorem used makes use of expansions in formal power series.
linear system implicit function theorem periodic solution hybrid system formal power series switched systems