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