Abstract
Explicit MPC of constrained linear systems is known to result in a piecewise ane controller and therefore also piecewise ane closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions oer a trade-o in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ) Lyapunov function is used for the stability verication of an of approximate explicit Model Predictive Control (MPC). A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise ane systems in general.
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