An improved ILMI method for static output feedback control with application to multivariable PID control

An improved iterative linear matrix inequality (ILMI) algorithm for static output feedback (SOF) stabilization problem without introducing any additional variables is proposed in this note. The proposed ILMI algorithm is also extended to solve the SOF H-infinity controller design problem. They are applied to the multivariable PID controllers. Numerical examples show that the proposed algorithms yield better results and faster convergence than the existing ones.