Fixed-Order Controller Design for Polytopic Systems Using Rank Deficiency in a Sylvester Matrix

Fixed-order controller design for LTI-SISO polytopic systems is investigated using rank deficiency constraint on the controller Sylvester resultant matrix. It is shown that the non-convexity of fixed-order controller design problem can be contracted in a rank deficiency constraint on Sylvester resultant matrix of the controller. Then, an improved convex approximation of the rank deficiency constraint is used that leads to a convex fixed-order controller design problem represented via LMIs. The effectiveness of the proposed method is shown by applying it to an experimental system.