Coprime factors, strictly positive real functions, LMI and low-order controller design for SISO systems

This paper develops a low-order controller design method requiring only the solution of a convex optimization problem. It addresses only linear continuous time-invariant single-input, single-output systems. The technique integrates several well-known results in control theory. An important step is the use of coprime factors so that based on strictly positive real functions, feedback stabilization using low-order controllers becomes a zero-placement problem which is convex. From this result, we develop algorithms to solve several optimal control problems, such as simultaneous pole-placement for several plants, H_∞ optimization, and H₂ optimization. Four example systems are used to illustrate the design algorithms