This text deals with the most fundamental deficiency of modern theory control: the lack of an easily applicable method for the design of low order controllers. It shows that solutions to many different problems in control all reduce to the same linear algebra problem. It employs matrix equalities and matrix inequalities in the solutions of fixed order control and also provides computational algorithms.
1. Introduction 2. Linear Algebra Review 3. Analysis of First-order Information 4. Second-order Information in Linear Systems 5. Covariance Controllers 6.Covariance Upper Boundary Controllers 7. H-Controllers 8. Model Reduction 9. Unified Perspective 10. Projection Methods 11. Successive Centring Methods 12. A: Linear Algebra Basics 13. B: Calculus of Vectors and Matrices 14. C: Balanced Model Reduction