An improvement on multivariable PID controller design via iterative LMI approach

This note improves the results of Zheng, Wang, and Lee (Automatica 38 (2002) 517) on the design of multivariable PID controllers via LMI approach. The idea of the improvement is to transform the problem of PID controller design to that of static output feedback (SOF) controller design for a system in descriptor form. The merits of the present result are: (1) The present condition removes the invertibility constraint on the controllers in Zheng et al. (2002) and incorporates it to the matrix inequality to be solved. (2) Once the SOF matrix is obtained, the PID gains are ready in hand and no additional computation is needed. (3) The present approach can deal with the case of some system parameters subject to perturbations.