Minimal order observer based H∞ controller design based on overbounding approximation method

In this paper, the minimal order observer based H
_∞
controller design is studied. The state space representation of the minimal order observer based controller is complicated and involves the product and quadratic terms of the decision variable matrices, i.e., the state feedback and observer gains. To make the design problem as a bilinear matrix inequality (BMI) problem, we represent the minimal order observer based controller by a descriptor representation, where the decision variable matrices are affinely involved. This descriptor representation enables us to design controllers by applying the overbounding approximation method for general BMI problems. The effectiveness of the proposed design procedure is demonstrated by a numerical example.