Nonlinear state feedback control of bilinear systems

The main contribution of this paper is the stabilization of bilinear systems by state feedback control. An extension of nonlinear feedback control based on the NonLinear Pole Placement technique (NLPP) is proposed. Then a polynomial feedback control approach is developed based on Linear Matrix Inequality resolution technique (LMI). Those approaches are applied on the two common classes of bilinear systems (non-homogeneous and homogeneous) in both cases of single and multi input. An example of vehicle suspension is then considered to illustrate the effectiveness of the proposed approaches.