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There are two main challenges in control of hybrid systems which are toguarantee the closed-loop stability and reduce computational complexity. Inthis paper, we propose the exponential stability conditions of hybrid systemswhich are described in the Mixed Logical Dynamical (MLD) form in closed-loopwith Model Predictive Control (MPC). To do this, it is proposed to use thedecreasing condition of infinity norm based Lyapunov function instead ofimposing the terminal equality constraint in the MPC formulation of MLD system.The exponential stability conditions have a better performance from bothimplementation and computational points of view. In addition, the exponentialstability conditions of the equilibrium point of the MLD system do not dependon the prediction horizon of MPC problem which is the main advantage of theproposed method. On the other hand, by using the decreasing condition of theLyapunov function in the MPC setup, the suboptimal version of the controlsignal with reduced complexity is obtained. In order to show the capabilitiesof the proposed method, the stabilization problem of the car suspension systemis studied.

Stable MPC Design for Hybrid Mixed Logical Dynamical Systems: $l_{\infty}$-based Lyapunov Approach