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I updated Chapter 11 again. This time, I introduced the concept of σ-finite Banach space valued measures and added a section on the dual of C(X,Y). Much of the results involving Banach space valued measures have been updated. I am still debating whether to include the section on product measure in Chapter 11 or in Chapter 12. I decided to put this version on my site rather than waiting for my decision on the section on product measure.
I have completed the revision of Chapter 11. Now the theory does not require that the underlying measure space is complete. This has the advantage of simplicity: one only need to work with Borel measurable sets if the functions to start with are Borel measurable. I have revised the definition of topological measure space to accommodate this change. This has led to a better approximation result in Lp spaces by continuous functions (Proposition 11.131).
The new Chapter 11 on measure and integration is not yet complete. I am still working on sections on product spaces, fundamental theorem of calculus, and Lp spaces. I have proof read Chapter 11 in the current version. So, the content are correct, even though incomplete.
In Chapter 10, I didn’t work out a general sensitivity theorem for optimization with equality constraints. This is because I can’t wait to start working on Chapter 11. Finally, I am getting to the integrals.
The minimum phase property will be necessary and sufficient for the disturbance attenuation problem in model reference control design. The necessity is proven in the paper. The sufficiency part will be constructive. It is easy to see that integrator backstepping methodology can be applied to this class of systems to design disturbance attenuating and stabilizing controllers.