# Version 2.9d

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## Contents |

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.

Additinal info:

- 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

## 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:

- 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 Example 5.5 and 5.6, m1 and m2 should be m
- Errata: In Examples 5.5 and 5.6, dynamics in modal form should use z, not x
- Errata: Equation (5.15) is linear in the initial conditions and *input*
- Errata: In Example 5.8, the third nodal equation should be deleted
- Errata: The labels for v2 and v3 are misplaced in Figure 5.12
- Errata: In AFM dynamics, c and k are missing subscript 2
- Errata: Missing factor of A in second term of equation (5.26)
- 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: 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 the last paragraph of Section 7.1, "reachable" should be replaced by "observable"
- Errata: In Example 7.2, the observer gain is given by equation (7.11)
- Errata: In Example 7.4, hats are missing in displayed equation for u
- Errata: In computation of error dynamics, u ff argument is missing
- Errata: Minus sign is missing in gain scheduled feedback
- 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: In section on pole/zero cancellations, pole and zero are at s = -a
- Errata: Location of the process pole is missing a zero in figure caption for cruise control example
- Errata: Missing parenthesis in exponential for output signal
- Errata: In description of Bode plot for second order transfer function, 'a' should be omega 0
- Errata: In Example 8.8, explanation of effects of poles and zeros is incorrect and confusing
- Errata: In Example 8.9, the expression for sigma is not correct
- Errata: Before Example 9.3, range of theta should be -pi/2 to pi/2
- Errata: In Theorem 9.3, N should be Z
- Errata: Missing factor of 2 pi in residue formula for proof of Theorem 9.3
- 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"
- Errata: Bennett's books on the history of control were published in 1979 and 1993