Krein Space

Abstract

In this monograph, linear estimation and control problems for systems with i/o delays are investigated under both the H₂ and H_∞ performance criteria. The key to our development is re-organized innovation analysis in Krein spaces. The reorganized innovation analysis approach, which forms the basis of the monograph, will be presented in Chapter 2. Krein space theory including innovation analysis and projections which can be found in [30], plays an important role in dealing with the H_∞ control and estimation problems as it provides a powerful tool to convert an H_∞ problem into an H₂ one under an appropriate Krein space. Thus, simple and intuitive techniques such as projections can be applied to derive a desired estimator or controller. For the convenience of discussions, in the rest of the monograph we shall first give a brief introduction to Krein space in this chapter.