This paper proposes a synthesis of a dynamic controller under constraints. It is based on model predictive control (MPC) approach and resolution of a convex optimisation problem with linear matrix inequalities (LMI). The controller guarantees the closed-loop stability for polytopic time-varying uncertain systems. Conditions are provided for the controller design based on the parameter dependent Lyapunov functions (PDLF). A new demonstration is developed based on the relaxation technique, to include a slack variables G i . The new LMI's formulation offers an additional degree of freedom for the controller design. Input and output constraints are also taken into account during the design of the controller. This approach allows varying and adjusting the dynamic of system by taking into account input/output constraints.

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