Robust PID controller design using BMI

The new BMI based method for robust stabilizing PID controller design for linear uncertain system is proposed. The general constrained structure of controller matrix is considered which is appropriate both for output feedback and decentralized control. The developed control design scheme aims at robust stabilization with guaranteed cost. The extended quadratic performance index is used including the first derivative of the state vector to damp oscillations. The obtained results use parameter-dependent Lyapunov function to reduce conservatism of robust stability conditions.