Robust Control Design for LTI Systems with Reduced Conservatism

The novel robust stability condition is proposed, appropriate for the structured uncertain system matrix with constant part. This is the case when dynamic robust controller is designed (e.g. PID) and the augmented system includes both uncertain controlled system and fixed part respective to controller dynamics. The developed condition is generally less conservative than the ones from literature. The structured auxiliary matrices are used with parameter dependent part respective to fixed part of augmented system matrix, which reduces conservatism of the robust stability condition. The resulting robust control design method apply BMI solver on the proposed stability condition. The qualities of the method are illustrated on randomly generated examples.