# Version 2.10c

This page contains information about version 2.10c of *Feedback Systems* by Karl J. Åström and Richard M. Murray. Version 2.10c contains corrections to the first printing through 4 March 2010. This revision corresponds to the third printing of the book.

Additional info and links:

- Revision date: 4 March 2010
- Complete book - this a PDF of the entire book, as a single PDF file (408 pages, 8 MB).
- Individual chapters: P, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, B
- Hyperlink version - this is a PDF of the entire book, with hypertext links on references for equations, figures, citations, etc.
*Note: the page numbers in this version are different from the print version.* - iPad optimized version - see the e-book page for information on how to use this file.

The electronic edition of *Feedback Systems* is provided with the permission of the publisher, Princeton University Press. This manuscript is for personal use only and may not be reproduced, in whole or in part, without written consent from the publisher.

## Errata

A full list of errata including page and line numbers is maintained on the errata page. The following errata have been identified in this version of the text (for a listing in page order, see version 2.10c errata):

- Errata: In Example 4.13, inequality should be for x 1 instead of x 2
- Errata: In Example 5.4, there is a sign error in one of the terms
- Errata: In equation (5.26), the u(k) term in the integral should be u(tau)
- Errata: After equation (5.31), rolling friction term disappears if v = 0
- Errata: In Exercise 5.8d, the left hand side of the first equation should be x(k+1)
- Errata: In Example 6.6 and 7.1, the output equation has 'x' for the state instead of 'c'
- Errata: In Example 6.8, the state space dynamics have errors in the trigonometric terms
- Errata: Diagonal entries for Q v should be rho
- Errata: Estimator dynamics in Theorem 7.3 are missing B k r r term
- Errata: Output in Kalman decomposition for Example 7.7 is missing state error term
- Errata: In equation (8.15), second order partial derivative is written incorrectly
- Errata: In Example 8.4, boundary condition and coefficients for psi(x) are incorrect
- Errata: Last equation in Example 8.6 has sign error in the second term
- Errata: In Exercise 8.5, k in the denominator of G(s) should be (k+1)
- Errata: Caption for Figure 10.3b should be "Derivative action"
- Errata: After equation (10.5), low frequency limit bound be 1/T d instead of T d
- Errata: The b k i term in the characteristic polynomial has an extra factor of s
- Errata: The PID integral time constant T i for the op amp implementation should be equal to R 2 C 2
- Errata: Dimensions of generalized process transfer function matrix should be 5x3
- Errata: Reference input not included in Figure 11.2 and dimensions of blocks are listed incorrectly
- Errata: In Figure 11.3, the label 'y' at the input to P 2 should be removed
- Errata: In expression for I 1, limits have an extra factor of i
- Errata: Contour integral in derivation of Bode's integral formula is analyzed incorrectly
- Errata: For Youla parameterization, P = b(s)/a(s) = B(s)/A(s) and C0 = G0(s)/F0(s)
- Errata: In Example 2.1, the state space equations for the balance system are missing a divisor of J t in one of the terms
- Errata: In Figure 2.7, the coefficients are for an update period of one day
- Errata: In the online version of the text, there is a formatting error in equation (3.23)
- Errata: In equation (3.26), q 0 is not defined

Note that errata in later versions of the text may also apply to this version. A full list of errata in all versions of the text is maintained on the errata page.