1996 Volume 32 Issue 1 Pages 45-54
A stabilization problem is considered for linear time-invariant systems interpolated with two nominal plants, where the controller is an interpolation of stabilizing controllers for the nominal plants. So far, a linear function is used as the interpolation, and the linearity restricts the class of stabilizable plants. Employing a bilinear function as the interpolation leads to some enlargement of the freedom of the controller design, although the cost of the implementation remains to be almost same as the linear case. Therefore, we consider the stabilization problem, where both the plant and the controller are interpolated bilinearly.
In the SISO case, a necessary and sufficient condition for the stabilization of the interpolated plants is derived based on the Nevanlinna-Pick interpolation problem. Furthermore, an LMI description of the condition gives a method to decide a feasible bilinear interpolation. In the MIMO case, a sufficient condition is formed as a strict positive realness condition, and the design method is also proposed with LMI conditions in the state-space form. The effectiveness of the proposed methods is shown with some examples in both cases.
