Abstract
A numerical optimization method of multivariable PID controllers that satisfy the performance index of the standard H∞ control problem is proposed. Since the problem is described as a bilinear matrix inequality of PID gains for each frequency, a new method of obtaining a sufficient condition in the form of a linear matrix inequality is proposed. The PID gain converges by solving the LMI problem iteratively starting from a stabilizing PID controller, while the H∞ norm decreases monotonically. Controller structure constraints such as decentralized control can be readily treated in the framework.
