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Toward optimal control of switched linear systems

We investigate the problem of driving the state of a switched linear control system between boundary states. We propose tight lower bounds for the minimum energy control problem. Furthermore, we show that the change of the system dynamics across the switching surface gives rise to phenomena that can be treated as a decidability problem of hybrid systems. Applying earlier results on controller synthesis for hybrid systems with linear continuous dynamics, we provide an algorithm for computing the minimum number of switchings of a trajectory from one state to another, and show that this algorithm is computable for a fairly wide class of linear switched systems.