Version 3.1.5

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This page contains information about version 3.1.5 of Feedback Systems by Karl J. Åström and Richard M. Murray. Version 3.1.5j is a preprint copy of the second edition of the text, which has been sent to the publisher for creation of final figures.

Additional info and links:

  • Revision date: 24 July 2020
  • Complete book - this a PDF of the entire book, as a single PDF file (573 pages, 35 MB).
  • Individual chapters: P, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 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.


A full list of errata including page and line numbers is maintained on the errata page.

Errata for this version only:

1-237In the air-fuel example in Section 1.8, missing reference to Figure 1.16bClosed
1-2325In Section 1.8, breaking should be brakingClosed
1-237In Section 1.7, there is a typo/missing word near the end of the sectionClosed
1-258In Section 1.8 text on paper mills, "production unit" should be "production units"Closed
1-258In the paper mill description in Section 1.8, "production unit" should be "production units"Closed
10-15In Section 10.3, the caption for Figure 10.11 seems to have a typoClosed
10-18In Section 10.4, Figure 10.14(b) seems to missing the curve for reverse driving phaseClosed
10-18In Section 10.4, the Figure 10.14 caption has a grammatical errorClosed
10-2-8In Section 10.1, there is a typo in the oscillation condition equationClosed
10-2-8In Equation 10.1, there's a typo 0 instead of ')'Duplicate
10-3-7In Section 10.1, the word "circuit" is misspelled.Closed
10-7In Section 10.2, part of Figure 10.5 seems to be missingClosed
11-128Ziegler-Nichols tuning rules don't quite match the original gains from the Ziegler-Nichols paperClosed
11-1322, 23Original Ziegler-Nichols gains listed after improved tuning rules are incorrectClosed
11-1322, 23Updated tuning rules are incorrect in equation (11.10b)Closed
11-16In Section 11.4, the Figure 11.10 caption has a typoClosed
11-519In Section 11.1, the word "frequencies" is duplicatedClosed
12-10-1In Section 12.2, there is a typo in the equation for P^+(s)Closed
12-101In Section 12.2, there is a singular vs. plural error when talking about the control signalClosed
12-112In Section 12.2, there is a typo in the equation for the approximate inverse of P(s)Closed
12-11-4In Section 12.2, the word "inherently" is misspelledClosed
12-11-4In Section 12.2, the sentence about sensitivity to model uncertainty has a grammatical issueClosed
12-14-5In Section 12.3, there is a missing spaceClosed
12-1611In Section 12.4, the word "limitations" is misspelledClosed
12-28In Section 12.6, there is a missing comma in the caption of Figure 12.17Closed
12-3-14In Section 12.1, the additional transfer functions for the F != 1 case seem to be incorrectClosed
12-3018In Section 12.6, a sentence in Theorem 12.2 is grammatically incorrectClosed
12-3511In Section 12.7, there's a grammatical error where it talks about the closed loop system H iClosed
12-354In Section 12.7, there's a typo in the discussion of inner/outer loop designClosed
12-4-5In Section 12.1, the vector w corresponding to Fig. 12.1 seems to be incorrectClosed
12-5In Section 12.2, the feedforward command u fv is mislabeled in Figure 12.3Closed
12-5-3In Section 12.2, the word "desired" is misspelledClosed
12-617In Section 12.2, the condition for Gyv being small seems to be misstatedClosed
13-1510In Section 13.3, the word "response" is duplicatedClosed
13-6-11In Section 13.2, the word "when" is incorrectly capitalizedClosed
13-78In Section 13.2, there's a grammatical issue in the discussion of system stabilityClosed
13-79In Section 13.2, the word "transfer" is misspelledClosed
13-79In Section 13.2, the word "point" is duplicatedClosed
13-8-9In Example 13.6 (Vinnicombe metric), the formula for conjugate point is missing a minus signClosed
2-1119In discussion on PI control in Section 2.2, incorrect formula for G yv when \omega is smallClosed
2-237In Section 2.1, there is a typo in the discussion of solving for an exponential inputClosed
2-49In Section 2.1, referred is misspelledClosed
2-55In Example 6.8, signalsith should be signals withClosed
2-7-12Equation (2.11) has the wrong formula for the transfer functionDuplicate
2-79Equation 2.11 is not equal to the preceding expression from which it cameClosed
2-812In Section 2.2, one too many parentheses in an expression for y(t)Closed
2-815Display equation above equation (2.12) has extra set of parenthesesClosed
2-913In discussion of proportional control in Section 2.2, missing v 0 in displayed equationClosed
3-1033In Section 3.1, there is a typo for pluralityClosed
3-10-8In discussion on algebraic loops in Section 3.2, there is an extra "be"Closed
... further results
"3.1.5" is not in the list of possible values (2.11c, 3.0h, 3.0i, 3.0j) for this property.