If you have suggestions or find errors in the course notes please send to b-hajek@illinois.edu. We will post here and send back to the authors at the end of the semester. Thank you!

• p. 7 Perhaps note that $I_1$ and $I_2$ are moments of inertia of the two links
• p. 24 Vector space axioms should include distributive properties: a*(x+y)=a*x + a*y and (a+b)*x=a*x+b*x
• p. 25 Third example of a vector space. $C^n[a,b], R)$ is the vector space of n-times continuously differentiable real-valued functions. This is a matter of notation, but the sentence in the text states the functions are real-valued and take values in R^n. Same comment applies to the next example -- the vector space $D^n$.
• On page 31, at the very bottom where the closed-form expression of \beta is shown, the top-right variable in the matrix, \alpha_{in}, should be \alpha_{1n}, and the bottom-left variable should be \alpha_{m1}.
• p. 37 Sixth line in the Section 2.9. "By orthogonality we then have" should be "By linearity we have" (No orthogonality is assumed/needed at that point.)
• p. 38 Seven lines before Section 2.10, the line contains "to to"
• p. 45 Problem 2.11.20. the vector x should be from complex n dimensional space not $\reals^n$
• p. 77 In the seventh line of the proof. It is stated that the gradient of $V$ is a row vector. Most other places in the book (and in the literature) gradients are column vectors. There are some transposes taken in some of the lines that follow which would not be there if the gradient were a column vector.
• p. 90 In the equation in line 8 just after "Equivalently, we must have" the lambda_i in the exponent should have a complex conjugate symbol over it (or a star).
• p. 171 The variable y in (10.9) should be replaced by t and supescript o should be on the x variables on the left hand . Moreover it would be better to add more to the notation to make clear that each side of the inequality is evaluated along a trajectory and the two derivatives are total derivatives. So it would be 0 = \ell(x^o(t),u^o(t),t) + \frac{d}{dt} \left( V^o(x^o(t),t)\right) \leq \ell(x(t),u(t),t) + \frac{d}{dt} \left( V^o(x(t),t)\right).
• p. 171 Four lines before Example 10.2.1, the apostrophe superscript on u in the integral should be removed.
• p. 173 First line -- should be "Since BR^{-1}B^T is semi positive definite
• p. 176 5-7 lines from bottom: The sentence "Note that if the eigenvalues of H are distinct then by Lemma 10.4 (i.e. if lambda is an eigenvalue then so is -lambda) none can lie on the j-omega axis" isn't true. (It is stated six lines before that that if the model is sabilizable and detectable then there are no purely imaginary eigenvalues.)
• p. 178 6 lines from end "ARE" is not defined until p. 181.
• p. 205 lines 6, 10, and 14: It should be $p^T(t)$ defined to equal the $\partial V^o / partial x. Later text switches correctly to gradients.
• p. 207 Figure 11.1: If could be a problem with the pdf reader but the gradient vectors don't show up well in Figure 11.1.
• p. 212 Something is wrong at the end of (11.14). A fix is to delete $\cal H$ and vector at end with $\dot{x}$ and $\dot{\lambda}). Or insert an equal sign before $\cal H$ and remove dots on x and lambda in the vector at the end.
• p. 218, the equations in part (b): $x_i(t_i)$ should be $x_i(t_1).$ In the next line it should be for $j\in I^c$ not for $i\in I^c.$. In (11.15) the second argument of (partial m)/(partial t) should be t_1 (i.e. add subscript 1 to t). In last equation five lines from bottom of the page the superscript T should be just after p: i.e. p^T(t) and not p(t)^T