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1 ## Copyright (C) 1998 Kai P. Mueller. |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {@var{retval} =} is_stabilizable (@var{sys}, @var{tol}) |
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21 ## @deftypefnx {Function File} {@var{retval} =} is_stabilizable (@var{a}, @var{b}, @var{tol}, @var{dflg}) |
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22 ## Logical check for system stabilizability (i.e., all unstable modes are controllable). |
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23 ## Returns 1 if the system is stabilizable, 0 if the system is not stabilizable, -1 |
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24 ## if the system has non stabilizable modes at the imaginary axis (unit circle for |
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25 ## discrete-time systems. |
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26 ## |
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27 ## Test for stabilizability is performed via Hautus Lemma. If |
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28 ## @iftex |
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29 ## @tex |
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30 ## @var{dflg}$\neq$0 |
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31 ## @end tex |
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32 ## @end iftex |
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33 ## @ifinfo |
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34 ## @var{dflg}!=0 |
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35 ## @end ifinfo |
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36 ## assume that discrete-time matrices (a,b) are supplied. |
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37 ## @seealso{size, rows, columns, length, ismatrix, isscalar, isvector |
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38 ## is_observable, is_stabilizable, is_detectable} |
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39 ## @end deftypefn |
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40 |
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41 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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42 ## Created: August 1993 |
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43 ## Updated by A. S. Hodel (scotte@eng.auburn.edu) Aubust, 1995 to use krylovb |
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44 ## Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 to accept systems |
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45 |
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46 function retval = is_stabilizable (a, b, tol, dflg) |
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47 |
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48 if(nargin < 1) |
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49 print_usage (); |
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50 elseif(isstruct(a)) |
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51 ## system passed. |
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52 if(nargin == 2) |
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53 tol = b; % get tolerance |
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54 elseif(nargin > 2) |
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55 print_usage (); |
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56 endif |
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57 disc = is_digital(a); |
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58 [a,b] = sys2ss(a); |
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59 else |
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60 ## a,b arguments sent directly. |
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61 if ((nargin > 4)||(nargin == 1)) |
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62 print_usage (); |
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63 endif |
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64 if(exist("dflg")) |
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65 disc = dflg; |
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66 else |
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67 disc = 0; |
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68 end |
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69 endif |
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70 |
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71 if(~exist("tol")) |
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72 tol = 200*eps; |
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73 end |
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74 |
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75 |
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76 ## Checking dimensions |
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77 n = is_square(a); |
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78 if (n==0) |
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79 error("is_stabilizable: a must be square"); |
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80 end |
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81 [nr,m] = size(b); |
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82 if (nr!=n) |
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83 error("is_stabilizable: (a,b) not conformal"); |
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84 end |
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85 |
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86 ##Computing the eigenvalue of A |
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87 L = eig(a); |
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88 retval = 1; |
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89 specflag = 0; |
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90 for i=1:n |
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91 if (disc==0) |
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92 ## Continuous time case |
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93 rL = real(L(i)); |
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94 if (rL>=0) |
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95 H = [eye(n)*L(i)-a, b]; |
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96 f = (rank(H,tol)==n); |
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97 if (f==0) |
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98 retval = 0; |
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99 if (rL==0) |
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100 specflag = 1; |
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101 end |
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102 end |
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103 end |
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104 else |
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105 ## Discrete time case |
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106 rL = abs(L(i)); |
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107 if (rL>=1) |
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108 H = [eye(n)*L(i)-a, b]; |
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109 f = (rank(H,tol)==n); |
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110 if (f==0) |
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111 retval = 0; |
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112 if (rL==1) |
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113 specflag = 1; |
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114 end |
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115 end |
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116 end |
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117 end |
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118 end |
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119 if (specflag==1) |
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120 ## This means that the system has uncontrollable modes at the imaginary axis |
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121 ## (or at the unit circle for discrete time systems) |
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122 retval = -1; |
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123 end |
