# Version 2.10b

This page contains information about version 2.10b of *Feedback Systems* by Karl J. Åström and Richard M. Murray. Version 2.10b contains corrections to the first printing through 22 February 2009. This revision corresponds to the second printing of the book.

Additional info and links:

- Revision date: 22 February 2009
- 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

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 2.10b errata):

- Errata: In Example 4.6, u d is not computed correctly
- Errata: In Example 4.11, Taylor series term is missing factor of 1/2
- Errata: Global Lyapunov stability requires additional conditions
- Errata: In the complex input u = exp(s t), s should be i omega, not i omega t
- Errata: Missing factor of B in displayed equation after equation (5.28)
- Errata: In equation (6.5), the 4, 3 entry of W r should be g m^2 l^2 M t/mu
- Errata: In Example 6.3, z 2 should be x 1/omega instead of x 2/omega
- Errata: Reference to equation (6.17) should be to equation (6.15)
- Errata: F R v F^T term dropped in proof of Theorem 7.4
- Errata: In Example 7.6, the coefficient in front of thetadot should be v/b
- Errata: In equation (7.25), the last two endpoint equations are not correct
- Errata: In Exercise 7.11, output to check is the feedforward signal
- Errata: In Exercise 7.13, missing equals sign in covariance specification
- Errata: In Example 8.3, a = 10 rad/s
- Errata: In Figure 8.3, the gain falls off at omega = a R1 k / R2
- Errata: Formula for Ged should not have the ' on dc and is missing a minus sign
- Errata: Formula for Ger should have the ' on dp, not dc
- Errata: In Figure 8.15 and accompanying text a should be omega0
- Errata: In Exercise 8.8, second transfer function should be G yn instead of G yd
- Errata: In Example 9.6, the critical gain is k = 0.5 instead of k = 1
- Errata: In Example 9.10, there is an extra factor of a in the second term of the step response
- Errata: In Example 11.9, the bound on the gain crossover frequency should be 6.48 rad/sec
- Errata: d(P 1, P 2) is the longest chordal distance, not shortest
- Errata: Riemann sphere has radius (not diameter) 1
- Errata: In Figure 12.8, the signs of A and B are reversed
- Errata: In Example 12.8, controller zero is at s = 3.5
- Errata: In Example 12.8, process zero is at s = -2
- Errata: In Example 12.9, poles are at -a, -p1, -p2
- Errata: After equation (12.23), generalized error is z, not w
- Errata: In Figure 2.16, theta should be O
- Errata: Equation (3.24) should have c in the numerator instead of c0
- Errata: In equation (3.27), the state used for the output should be c, not x
- Errata: Equation (4.4) is labeled incorrectly

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.