  In this paper, we develop a systematic method for constructing a generalized
discrete-time control Lyapunov function for the flexible-step Model Predictive
Control (MPC) scheme, recently introduced in [3], when restricted to the class
of linear systems. Specifically, we show that a set of Linear Matrix
Inequalities (LMIs) can be used for this purpose, demonstrating its
tractability. The main consequence of this LMI formulation is that, when
combined with flexible-step MPC, we can effectively stabilize switched control
systems, for which no quadratic common Lyapunov function exists.
