Abstract:This paper sketches the history for application of LMI in control theory, emphasizes the principle of LMI and the importance for its application in robust predictive control synthesis approach, and illustrates how to apply LMI in a new synthesis approach of robust predict control via an example. This paper can serve as a reference for applying LMI in robust predictive control and carrying out robust predictive control algorithm on microcomputer. Keywords:LMI, convex problem, robust predictive control