# Version 2.9d

This page contains information about version 2.9d of *Feedback Systems* by Karl J. Åström and Richard M. Murray. Version 2.9d corresponds to the version of the book that was sent to press. It became available for purchase in hardcopy in April 2008. See the Main Page for links to booksellers.

Additional info and links:

- Revision date: 30 January 2008
- 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 2.9d errata):

- Errata: The Wright brothers made their first successful flight in 1903, not 1905
- Errata: In discussion on disturbance signals, "can" should be "cannot"
- Errata: In Exercises 2.4 and 5.9, the (2,1) entry of the dynamics matrix should be ab-b
- Errata: In Exercise 2.7, reference to inverted pendulum may be confusing
- Errata: In Equation (3.19), the second term in the window dynamics should contain \rho c
- Errata: In Exercise 3.2: use observable form, delta is the steering angle and "title" should be "tilt"
- Errata: State space dynamics in Exercise 3.5 are not correct
- Errata: Solution for x 2j in block diagonal form discussion has sign errors
- Errata: Closed loop dynamics matrix is incorrect in Example 4.6
- Errata: Missing γ in equation (4.9)
- Errata: In Example 4.8, the linearized dynamics should contain 3 r e, not 2 r e
- Errata: In Example 4.9, V(x) should be V(z)
- Errata: Typo in the caption for Figure 4.15
- Errata: In Exercise 4.1, tau should be defined as t-t 0
- Errata: In Exercise 4.1, x 0 should not be subtracted from time-shifted solution
- Errata: In Exercise 4.2, a e should be a
- Errata: Sign error in second Lyapunov function in Exercise 4.4
- Errata: In Exercise 4.6, Pm/J should be taken as 1 and factor of 1/2 is misplaced
- Errata: In Exercise 4.14c, the transformation T and its inverse are swapped
- Errata: Extraneous text "!linear" in Section 5.1
- Errata: In equation (5.5), the upper limit of the integral should be t
- Errata: Example 5.5 includes a damping term not shown in Figure 5.4
- Errata: In Examples 5.5 and 5.6, dynamics in modal form should use z, not x
- Errata: In Figure 1.11, caption refers to "numbers in circles" that are not present in figure
- Errata: In AFM dynamics, c and k are missing subscript 2
- Errata: Parameter values are missing in Exercise 5.3
- Errata: Remove part (a) in Exercise 5.6
- Errata: In Exercise 5.7, the 5% settling time should be 3 tau instead of 2 tau
- Errata: In Exercise 5.8, the initial condition is x 0
- Errata: In heuristic derivation of reachability test, α is missing subscript
- Errata: Formula for k r in equation (6.21) of Theorem 6.3 is incorrect
- Errata: Missing 's' in expression for characteristic polynomial in discussion of eigenvalue assignment
- Errata: In equation (6.22), k omega^2 should be k omega 0^2
- Errata: In equation (6.24), the sign of the sin(omega t) term is incorrect for zeta less than one
- Errata: Values of zeta in the caption for Figure 6.8 don't match the figure
- Errata: Dynamics matrix in Example 6.7 has errors in (3,4) and (4,4) entries
- Errata: In Example 6.7, the A matrix has an error in the (3,4) entry
- Errata: Numerical gains for Example 6.7 are incorrect
- Errata: In Exercise 6.4, need to assume A is invertible and C A^-1 B is nonzero
- Errata: In Exercise 6.13, R should be removed and rho should be rho 1
- Errata: In computation of error dynamics, u ff argument is missing
- Errata: References to first and second equations are switched in computer implementation discussion
- Errata: Explanation of the lack of zeros when B or C is full rank is confusing
- Errata: Sign error in equation (8.17) - (sI - A) should be (A - sI)
- Errata: In Example 8.5, q should be replaced by theta
- Errata: Location of the process pole is missing a zero in figure caption for cruise control example
- Errata: Caption for Figure 8.15b is missing an s in the numerator
- Errata: In Theorem 9.3, N should be Z
- Errata: Exponential signal is incorrect on the left-hand side of harmonic expansion equation
- Errata: In Exercise 9.9, 10/a should be 1/tau
- Errata: Toward end of Section 10.4, k i should be k t
- Errata: Figure 10.11 is missing filter on derivative term
- Errata: In Figure 10.13, the indices on the resistors and capacitors are incorrect
- Errata: Missing ydot after equation (10.16)
- Errata: In Exercise 10.1, the second term in the denominator should be kp not kd
- Errata: In Exercise 10.11, the dynamics for x 2 should test for e less than e 0, not e less than 1
- Errata: Extraneous 'LDH' and comment in the text
- Errata: Arrow labeled u fd in Figure 11.3 is in the wrong direction
- Errata: The signal u ff should be u fr in the caption for Figure 11.3 and associated text
- Errata: Extraneous text "!design" in Chapter 12
- Errata: Maximum sensitivity occurs at frequency omega ms not omega sc
- Errata: Proportional gain in Example 11.4 transfer function should be kp
- Errata: Denominator of vectored thrust process model should be Js^2
- Errata: Exercise 11.4 should be Example 11.4 in Exercise 11.9
- Errata: Numerator and denominator are switched in Exercise 11.11
- Errata: T d should be T f in Exercise 11.9
- Errata: Caption for Figure 12.4 doesn't quite match figure
- Errata: In Example 12.6, n = -1 should be n = 1
- Errata: "Assigning a closed loop zero" should be "assigning a closed loop pole"

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.