## Solutions Manual for Classical Feedback Control with MATLAB by Lurie Enright

By Lurie Enright

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**Example text**

1 Generating vectors The expression 1:5 is the row vector [1 2 3 4 5]. The numbers need not be integers, and the increment need not be one. 2 and 5:-1:1 gives [5 4 3 2 1] with an increment of -1. 1. Be careful how you mix the colon operator with other operators. Compare 1:5-3 with (1:5)-3. In general, the expression lo:hi is the sequence [lo, lo+1, lo+2, …, hi] except that the last term in the sequence is always less than or equal to hi if either one are not integers. 1 is [1 2 3 4 5]. The sequence is empty if lo > hi.

They look at the matrix and try to pick the best method. The linsolve function acts like \, except that you can tell it about your matrix. Try: A = [1 2 ; 3 4] b = [4 10]' A\b linsolve(A,b) 25 In both cases, you get solution x=[2;1] to the linear system A*x=b. If A is symmetric and positive definite, one explicit solution method is to perform a Cholesky factorization, followed by two solves with triangular matrices. Try: C = [2 1 ; 1 2] x = C\b Here is an equivalent method: R = chol(C) y = R'\b x = R\y The matrix R is upper triangular, but MATLAB explicitly transposes R and then determines for itself that R' is lower triangular.

This type of cell has nothing to do with cell arrays, but defines a section of code in an M-file. Cells can be executed by themselves, and cell publishing (discussed in Chapter 20) generates reports whose sections are defined by an M-file’s cells. 7 MATLAB’s path M-files must be in a directory accessible to MATLAB. M-files in the current directory are always accessible. The current list of directories in MATLAB’s search path is obtained by the command path. This command can also be used to add or delete directories from the search path.