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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.
Fürnsinn et al. (Thu,) studied this question.