TOOLS FOR CONTROL SYSTEM DESIGN — STRATIFICATION OF MATRIX PAIRS AND PERIODIC RICCATI DIFFERENTIAL EQUATION SOLVERS

iii iv Modern control theory is today an interdisciplinary area of research. Just as much as this can be problematic, it also provides a rich research environment where practice and theory meet. This Thesis is conducted in the borderline between computing sci-ence (numerical analysis) and applied control theory. The design and analysis of a modern control system is a complex problem that requires high qualitative software to accomplish. Ideally, such software should be based on robust methods and numerical stable algorithms that provide quantitative as well as qualitative information. The introduction of the Thesis is dedicated to the underlying control theory and to introduce the reader to the main subjects. Throughout the Thesis, the theory is illus-trated with several examples, and similarities and differences between the terminology from mathematics, systems and control theory, and numerical linear algebra are high-lighted. The main contributions of the Thesis are structured in two parts, dealing wit