Pole assignment in LMI regions for linear constrained control systems

This paper is devoted to the pole assignment problem in LMI regions for linear non symmetrical constrained control systems. First, the eigenvalue clustreing problem in LMI regions for complex matrices is studied. Hence, the study is extended to the case of polytopic uncertainties. Second, the synthesis of stabilizing controllers for linear constrained control systems assigning the closed loop poles in specified LMI regions is achieved. The concept of positive invariance is used and it is shown that it is suitable for non symmetrical constrained control systems. Examples are given throughout the paper to illustrate our approach.