Appendix A: Conjugate Points and Existence of Value

Abstract

We provide in the first part of this appendix a self-contained introduction to conjugate points as they arise in dynamic linear-quadratic optimization, and in particular in the context of finite-horizon linear-quadratic differential games. In the second part we present the counterpart of these results in the infinite horizon, where also the issue of stability becomes important. The material included in this appendix is used extensively in Chapter 4, in the proof of some key results in the solution of the continuous-time disturbance attenuation problem, and also partly in Chapters 5, 7, and 8.