Design of Q-filters for disturbance observers via BMI approach

The type-k disturbance observer, also known as high order disturbance observer, is a robust output feedback controller which can reject polynomial-in-time disturbances exactly and at the same time unmodeled disturbances approximately. To ensure the robust stability of the closed-loop system, the key component of the controller called Q-filter should be designed appropriately. In this paper, we formulate the design problem in terms of a set of bilinear matrix inequalities so that the coefficients of Q-filters are chosen simultaneously. The solution from the proposed method can be less conservative compared to the recursive design procedure developed recently.