Tracking and Regulation III: Structurally Stable Synthesis

Abstract

In this chapter we investigate the regulator problem with internal stability (RPIS) discussed in Chapter 7, from the viewpoint of well-posedness and genericity in the sense of Section 0.16, and of structurally stable implementa-tion. Subject to mild restrictions it is shown that, if and only if RPIS is well-posed, a controller can be synthesized which preserves output regula-tion and loop stability in the presence of small parameter variations, of a specified type, in controller and plant. Synthesis is achieved by means of a feedback configuration which, in general, incorporates an invariant, and suitably redundant, copy of the exosystem, namely the dynamic model adopted for the exogenous reference and disturbance signals which the system is required to process. The geometric idea underlying these results is transversality, or the intersection of subspaces in general position.