ROBUST OUTPUT ONE AHEAD MODEL PREDICTIVE CONTROL DESIGN Vojtech Vesel´ y and Danica Rosinov´ a 1 Slovak University of Technology, Faculty of Electrical Engineering and IT, URPI, Bratislava, Slovak Republic, E-mail : vojtech.vesely@stuba.sk Abstract: The paper addresses the problem of designing a parameter dependent quadratic stability output/state feedback model predictive control for linear polytopic systems without constraints. Keywords: Model predictive control, Robust Control, Parameter dependent quadratic stability, Lyapunov function, Polytopic system 1. INTRODUCTION Model predictive control (MPC) has attracted notable attention in control of dynamic systems. The idea of MPC can be summarized as follows, (Camacho and Bordons, 2004; Maciejovski, 2002, Rositer, 2003): • Predict the future behaviour of the process state/output over the finite time horizon. • Compute the future input signals on line at each step by minimizing a cost function under inequality constraints on the manipu- lated (control) and/or controlled variables. • Apply on the controlled plant only the first of vector control variable and repeat the previous step with new measured in- put/state/output variables. Therefore, the presence of the plant model is a necessary condition for the development of the predictive control. The success of MPC depends on the degree of precision of the plant model. In the most references the principal shortcoming of existing MPC-based control techniques is their inability to explicitly incorporate plant model un- certainty, Kothare et al, 1996. Thus, the present state of robustness problem in MPC can be sum- 1 Supported by the Grant Agency of the Slovak Republic under Grant 1/3841/06 marized as follows: Analysis of robustness properties of MPC. Zafiriou nad Marchal, 1991 have used the contrac- tion properties of MPC to developed necessary- sufficient conditions for robust stability of MPC with input and output constraints for SISO sys- tems and impulse response model. Polak and Yang, 1993 have analyzed robust stability of MPC using a contraction constraint on the state. MPC with explicit uncertainty description. Zheng and Morari, 1993, have presented robust MPC schemes for SISO FIR plants, given un- certainty bounds on the impulse response co- efficients. Some MPC consider additive type of uncertainty, de la Pena et al, 2005 or paramet- ric (structured) type uncertainty using CARIMA model and linear matrix inequality, Bouzouita et al, 2007. In Lovaas et al, 2007 for open-loop stable systems having input constraints the unstructured uncertainty is used. The robust stability can be established by choosing the large value for the control input weighting matrix R in the cost func- tion. The authors proposed a new less conserva- tive stability test for determining a sufficiently large control penalty R using bilinear matrix in- equality (BMI). The other technique- constrained tightening to design of robust MPC have been proposed in Kuwata et al, 2007. Above approaches are based on idea of increasing the robustness