On the design of multivariable PID controllers via LMI approach

In the past decades, we have witnessed the developments of various kinds of modern or postmodern control theories, such as LQG or LQR optimal control, H∞ control, and μ analysis and synthesis, from their emergence to maturity and applications in some practical systems. Despite of the success of the modern or postmodern control theory, we have to admit that the majority of the controllers used in industry are of classical proportional-plus-integral-derivative (PID) type. This is mainly due to its relatively simple structure, ready-in-hand implementation, and perhaps, being easily understood. Therefore it is often the case that one first considers PID controllers in practical applications unless evidence shows that they are insufficient to meet specifications.