Linear Controller Design: Limits of Performance Via Convex Optimization

Abstract

We give a tutorial presentation of an approach to the analysis and design of linear control systems based on numerical convex optimization over closed-loop maps. Convexity makes numerical solution effective: it is possible to determine whether or not there is a controller that achieves a given set of specifications. Thus, the limit of achievable performance can be computed. Although the basic idea behind this approach can be traced back into the 1950s, two developments since then have made it more attractive and useful. This first is a simple description of. the achievable closed-loop behaviors for systems with multiple sensors and actuators. The second is the development of numerical algorithms for solving convex optimization problems, and powerful computers to run them. © 1990 IEEE