  The paper presents a novel method for designing an optimal controller for
discrete-time switched linear systems. The problem is formulated as one of
computing the discrete mode sequence and the continuous input sequence that
jointly minimize a quadratic performance index. State-of-art methods for
solving such a control problem suffer in general from a high computational
requirement due to the fact that an exponential number of switching sequences
must be explored. The method of this paper addresses the challenge of the
switching law design by introducing auxiliary continuous input variables and
then solving a non-smooth block-sparsity inducing optimization problem.
