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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 the pair(a,b) is controllable, then return value is the |
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6 # dimension of x. 0therwise, returns a value of 0 |
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7 # |
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8 # See also: size, rows, columns, length, is_matrix, is_scalar, is_vector |
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9 |
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10 # This should really use the method below, but I'm being lazy for now: |
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11 # |
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12 # Controllability is determined by applying Arnoldi iteration with complete |
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13 # re-orthogonalization to obtain an orthogonal basis of the Krylov subspace |
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14 # n-1 |
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15 # span([b,a*b,...,a^ b]). tol is a roundoff paramter, |
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16 # set to 2*eps if omitted |
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17 |
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18 if ((nargin == 2) || (nargin == 3)) |
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19 n = is_square(a); |
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20 [nr, nc] = size (b); |
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21 if((n == 0) || (n != nr) || (nc == 0)) |
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22 retval = 0; |
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23 else |
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24 |
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25 m = b; |
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26 tmp = b; |
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27 for ii=1:(n-1) |
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28 tmp = a*tmp; |
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29 m = [m,tmp]; |
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30 endfor |
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31 |
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32 # if n is of any significant size, m will be low rank, so be careful! |
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33 if(nargin == 3) |
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34 if(is_scalar(tol)) |
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35 retval = (rank(m,tol) == n); |
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36 else |
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37 error('is_controllable: tol must be a scalar') |
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38 endif |
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39 else |
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40 retval = (rank(m) == n); |
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41 endif |
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42 endif |
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43 else |
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44 error ("usage: is_controllable (a,b)"); |
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45 endif |
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46 |
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47 endfunction |
