1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

https://www.control.utoronto.ca/people/profs/francis/dft.pdf

Feedback Control Theory

Bounded linear operators Interpolation of Banach spaces Integral operators on $L^p$ spaces Bergman spaces Bloch and Besov spaces The Berezin transform Toeplitz operators on the Bergman space Hankel operators on the Bergman space Hardy spaces and BMO Hankel operators on the Hardy space Composition operators Bibliography Index.

http://www.gbv.de/dms/goettingen/52319126X.pdf

Operator theory in function spaces

This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.

The geometry of fractal sets

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set.The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

https://abel.math.harvard.edu/~ctm/papers/home/text/papers/real/book.pdf

Complex Dynamics and Renormalization

Preliminaries.- Hp Spaces.- Conjugate Functions.- Some Extremal Problems.- Some Uniform Algebra.- Bounded Mean Oscillation.- Interpolating Sequences.- The Corona Construction.- Douglas Algebras.- Interpolating Sequences and Maximal Ideals.

Bounded Analytic Functions

Analytic capacity.- The cauchy transform.- Hausdorff measure.- Some examples.- Applications to approximation.

https://www.springer.com/productFlyer_978-3-540-06073-4.pdf?SGWID=0-0-1297-173761499-0

Analytic capacity and measure

Then clearly BMO c BMO, with \\φ\\d £\\φ\\, but BMO and BMO, are not the same space; the function log\x9 \X{ttlj>0] is in BMO, but not in BMO. In analysis BMO is more important than BMO, because BMO is translation invariant, but BMO, is not. On the other hand, BMO, is very much the easier space to work with because dyadic cubes are nested (if two open daydic cubes intersect then one of them is contained in the other). For example, for BMO the original proofs [1], [6], [8], [11] of the four theorems stated below were rather technical, while for BMO, the analogous results are comparatively trivial. In this paper we derive the four theorems from their dyadic counterparts. Here is the idea. Let Taφ(x) = φ(x — a). Then

https://msp.org/pjm/1982/99-2/pjm-v99-n2-p08-s.pdf

BMO from dyadic BMO

Gaps and bands of one dimensional periodic Schrödinger operators, II

(9dx T I -III XI~ is the mean of cp over I. Every bounded (measurable) function is in BMO and IIpII* 0 and x0 =x(s) such that (1.2) sup, 1 | {x G I: I 9(x) -' l > A} I < e-/'

John Garnett

Papers

Bounded Analytic Functions

Analytic capacity and measure

BMO from dyadic BMO

Gaps and bands of one dimensional periodic Schrödinger operators, II

The Distance in BMO to L