Book

Control and system theory of discrete-time stochastic systems,
Springer Nature Switzerland AG, Cham, 2021.
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Book extension

 The book extension contains primarily all corrections discovered so far in the book.
In addition, the book extension contains notes about references, examples, and
proofs which were not included in the book for various reasons.
References are provided primarily in the Chapters 8, 19, and 14.
Examples are provided in the Chapters 12 and 13, and
a proof is provided in Chapter 14.
bookcontrolstocdted1e.20220815.pdf.
bookcontrolstocdted1e.20220124.pdf.

Comments on the Kalman Filter

 The Sections `Time-Varying Kalman Filter' and `Conditional Kalman Filter'.
Theorem 8.3.2 about the Kalman filter and Theorem 8.10.1 about the conditional Kalman filter are closely related to Theorem 13.3 on p. 63 and Theorem 13.4 on p. 65 of Volume II of the book by R.S. Liptser and A.N. Shiryayev. Those authors treat the case in which the variance of the measurement noise can be singular which special case is not treated in this book.

My apologies to the authors R.S. Liptser and A.N. Shiryayev for this lack of proper referencing.

It is to be noted that the Theorems 13.3 and 13.4 of the book of Liptser and Shiryayev 1977. are based on a different system representation than that used in this book. Compare the equations (13.46) and (13.47) of that reference with the equations of Def. 4.3.1 of this book. It is well known that these two system representations cannot be converted into each other. Consequently, there exist two different system representations and two different corresponding Kalman filter representations. The system representation used in this book is in accordance with the literature for the system representation used in Europe and in North-America.

The proofs of the Theorems 8.3.2 and 8.10.1 of this book make use of Proposition 19.7.4 of this book. It is mentioned in Chapter 19 of this edition 1.E that Proposition 19.7.4 on p. 743 of this book is a special case of Theorem 13.3 and 13.4 of the book by Liptser and Shiryayev 1977. However, the proof of Proposition 19.7.4 of this book differs from the proofs of the mentioned theorems of the book by Liptser and Shiryayev 1977. The proofs of Theorem 8.3.2 and of Theorem 8.10.1 of this book are otherwise closely related to those of the book by Liptser and Shiryayev 1977.

Last update 18 August 2022.
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