Minimum Order Feedback Control

Conside a linear time-invariant state space system \[ \dot{x}(t)=A x(t) +B u(t), \quad y=C x(t) \] with the system matrix $A$, the input matrix $B$ and the output matrix $C$. From the viewpoint of implementation, a static output feedback controller \[ u(t)=K y(t) \] with a constant gain matrix $K$ is the simplest way to control the system. However, this controller may not achieve the desired design goals (e.g. full eigenvalue placement). Alternatively, we could use a controller of dynamic order $q$ described by \[ \dot{z}(t)=Fz(t)+Gy(t),\quad u(t)=Hz(t)+Ky(t), \] where $q=\dim z$. The static output feedback controller can be seens as a special case with $q=0$.

In [1], a new approach for static output feedback controller design was presented. We employed the Gauss-Newton method to computed the gain matrix [2]. The above mentioned approach was extended to minimum order controller design in [3].


  1. Franke, M.: Eigenvalue assignment by static output feedback–on a new solvability condition and the computation of low gain feedback matrices.
    International Journal of Control, 87 (1) 2014, 64-75.
  2. Franke, M., Röbenack, K.: Calculation of constant output feedback matrices for pole placement by a Gauss-Newton method.
    Control and intelligent Systems, 42 (3) 2014, 225-230.
  3. Franke, M., Röbenack, K.: Pole placement by dynamic output feedback of minimal order.
    PAMM, 14 (1) 2014, 885-886.