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1 function retval = is_controllable (a,b,tol) |
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2 |
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3 # usage: is_controllable (a,b{,tol}) |
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4 # |
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5 # Returns 1 if the pair (a, b) is controllable, or 0 if not. |
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6 # |
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7 # See also: size, rows, columns, length, is_matrix, is_scalar, is_vector |
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8 |
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9 # This should really use the method below, but I'm being lazy for now: |
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10 # |
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11 # Controllability is determined by applying Arnoldi iteration with |
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12 # complete re-orthogonalization to obtain an orthogonal basis of the |
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13 # Krylov subspace |
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14 # n-1 |
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15 # span ([b,a*b,...,a^ b]). |
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16 # |
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17 # tol is a roundoff paramter, set to 2*eps if omitted |
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18 |
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19 if (nargin == 2 || nargin == 3) |
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20 |
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21 n = is_square (a); |
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22 [nr, nc] = size (b); |
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23 |
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24 if (n == 0 || n != nr || nc == 0) |
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25 retval = 0; |
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26 else |
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27 |
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28 m = b; |
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29 tmp = b; |
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30 for ii = 1:(n-1) |
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31 tmp = a * tmp; |
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32 m = [m, tmp]; |
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33 endfor |
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34 |
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35 # If n is of any significant size, m will be low rank, so be careful! |
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36 |
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37 if (nargin == 3) |
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38 if (is_scalar (tol)) |
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39 retval = (rank (m, tol) == n); |
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40 else |
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41 error ("is_controllable: tol must be a scalar"); |
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42 endif |
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43 else |
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44 retval = (rank (m) == n); |
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45 endif |
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46 endif |
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47 else |
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48 error ("usage: is_controllable (a, b)"); |
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49 endif |
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50 |
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51 endfunction |
