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1 ## Copyright (C) 1996, 1998, 2000, 2002, 2004, 2005, 2007 |
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2 ## Auburn University. All rights reserved. |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist}) |
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22 ## Create system structure from state-space data. May be continuous, |
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23 ## discrete, or mixed (sampled data) |
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24 ## |
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25 ## @strong{Inputs} |
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26 ## @table @var |
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27 ## @item a |
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28 ## @itemx b |
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29 ## @itemx c |
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30 ## @itemx d |
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31 ## usual state space matrices. |
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32 ## |
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33 ## default: @var{d} = zero matrix |
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34 ## |
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35 ## @item tsam |
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36 ## sampling rate. Default: @math{tsam = 0} (continuous system) |
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37 ## |
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38 ## @item n |
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39 ## @itemx nz |
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40 ## number of continuous, discrete states in the system |
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41 ## |
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42 ## If @var{tsam} is 0, @math{n = @code{rows}(@var{a})}, @math{nz = 0}. |
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43 ## |
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44 ## If @var{tsam} is greater than zero, @math{n = 0}, |
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45 ## @math{nz = @code{rows}(@var{a})} |
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46 ## |
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47 ## see below for system partitioning |
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48 ## |
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49 ## @item stname |
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50 ## cell array of strings of state signal names |
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51 ## |
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52 ## default (@var{stname}=[] on input): @code{x_n} for continuous states, |
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53 ## @code{xd_n} for discrete states |
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54 ## |
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55 ## @item inname |
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56 ## cell array of strings of input signal names |
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57 ## |
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58 ## default (@var{inname} = [] on input): @code{u_n} |
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59 ## |
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60 ## @item outname |
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61 ## cell array of strings of input signal names |
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62 ## |
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63 ## default (@var{outname} = [] on input): @code{y_n} |
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64 ## |
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65 ## @item outlist |
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66 ## |
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67 ## list of indices of outputs y that are sampled |
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68 ## |
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69 ## If @var{tsam} is 0, @math{outlist = []}. |
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70 ## |
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71 ## If @var{tsam} is greater than 0, @math{outlist = 1:@code{rows}(@var{c})}. |
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72 ## @end table |
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73 ## |
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74 ## Unlike states, discrete/continuous outputs may appear in any order. |
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75 ## |
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76 ## @code{sys2ss} returns a vector @var{yd} where |
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77 ## @var{yd}(@var{outlist}) = 1; all other entries of @var{yd} are 0. |
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78 ## |
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79 ## @strong{Outputs} |
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80 ## @var{outsys} = system data structure |
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81 ## |
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82 ## @strong{System partitioning} |
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83 ## |
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84 ## Suppose for simplicity that outlist specified |
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85 ## that the first several outputs were continuous and the remaining outputs |
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86 ## were discrete. Then the system is partitioned as |
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87 ## @example |
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88 ## @group |
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89 ## x = [ xc ] (n x 1) |
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90 ## [ xd ] (nz x 1 discrete states) |
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91 ## a = [ acc acd ] b = [ bc ] |
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92 ## [ adc add ] [ bd ] |
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93 ## c = [ ccc ccd ] d = [ dc ] |
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94 ## [ cdc cdd ] [ dd ] |
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95 ## |
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96 ## (cdc = c(outlist,1:n), etc.) |
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97 ## @end group |
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98 ## @end example |
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99 ## with dynamic equations: |
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100 ## @ifinfo |
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101 ## @math{d/dt xc(t) = acc*xc(t) + acd*xd(k*tsam) + bc*u(t)} |
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102 ## |
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103 ## @math{xd((k+1)*tsam) = adc*xc(k*tsam) + add*xd(k*tsam) + bd*u(k*tsam)} |
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104 ## |
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105 ## @math{yc(t) = ccc*xc(t) + ccd*xd(k*tsam) + dc*u(t)} |
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106 ## |
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107 ## @math{yd(k*tsam) = cdc*xc(k*tsam) + cdd*xd(k*tsam) + dd*u(k*tsam)} |
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108 ## @end ifinfo |
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109 ## @iftex |
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110 ## @tex |
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111 ## $$\eqalign{ |
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112 ## {d \over dt} x_c(t) |
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113 ## & = a_{cc} x_c(t) + a_{cd} x_d(k*t_{sam}) + bc*u(t) \cr |
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114 ## x_d((k+1)*t_{sam}) |
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115 ## & = a_{dc} x_c(k t_{sam}) + a_{dd} x_d(k t_{sam}) + b_d u(k t_{sam}) \cr |
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116 ## y_c(t) |
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117 ## & = c_{cc} x_c(t) + c_{cd} x_d(k t_{sam}) + d_c u(t) \cr |
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118 ## y_d(k t_{sam}) |
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119 ## & = c_{dc} x_c(k t_{sam}) + c_{dd} x_d(k t_{sam}) + d_d u(k t_{sam}) |
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120 ## }$$ |
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121 ## @end tex |
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122 ## @end iftex |
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123 ## |
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124 ## @strong{Signal partitions} |
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125 ## @example |
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126 ## @group |
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127 ## | continuous | discrete | |
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128 ## ---------------------------------------------------- |
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129 ## states | stname(1:n,:) | stname((n+1):(n+nz),:) | |
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130 ## ---------------------------------------------------- |
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131 ## outputs | outname(cout,:) | outname(outlist,:) | |
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132 ## ---------------------------------------------------- |
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133 ## @end group |
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134 ## @end example |
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135 ## where @math{cout} is the list of in 1:@code{rows}(@var{p}) |
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136 ## that are not contained in outlist. (Discrete/continuous outputs |
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137 ## may be entered in any order desired by the user.) |
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138 ## |
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139 ## @strong{Example} |
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140 ## @example |
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141 ## octave:1> a = [1 2 3; 4 5 6; 7 8 10]; |
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142 ## octave:2> b = [0 0 ; 0 1 ; 1 0]; |
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143 ## octave:3> c = eye (3); |
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144 ## octave:4> sys = ss (a, b, c, [], 0, 3, 0, @{"volts", "amps", "joules"@}); |
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145 ## octave:5> sysout(sys); |
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146 ## Input(s) |
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147 ## 1: u_1 |
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148 ## 2: u_2 |
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149 ## |
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150 ## Output(s): |
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151 ## 1: y_1 |
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152 ## 2: y_2 |
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153 ## 3: y_3 |
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154 ## |
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155 ## state-space form: |
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156 ## 3 continuous states, 0 discrete states |
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157 ## State(s): |
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158 ## 1: volts |
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159 ## 2: amps |
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160 ## 3: joules |
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161 ## |
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162 ## A matrix: 3 x 3 |
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163 ## 1 2 3 |
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164 ## 4 5 6 |
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165 ## 7 8 10 |
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166 ## B matrix: 3 x 2 |
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167 ## 0 0 |
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168 ## 0 1 |
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169 ## 1 0 |
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170 ## C matrix: 3 x 3 |
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171 ## 1 0 0 |
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172 ## 0 1 0 |
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173 ## 0 0 1 |
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174 ## D matrix: 3 x 3 |
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175 ## 0 0 |
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176 ## 0 0 |
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177 ## 0 0 |
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178 ## @end example |
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179 ## Notice that the @math{D} matrix is constructed by default to the |
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180 ## correct dimensions. Default input and output signals names were assigned |
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181 ## since none were given. |
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182 ## @end deftypefn |
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183 |
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184 ## Author: John Ingram <ingraje@eng.auburn.edu> |
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185 ## Created: July 20, 1996 |
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186 |
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187 function retsys = ss2sys (varargin ) |
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188 |
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189 warning("ss2sys is deprecated. Use ss() instead."); |
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190 retsys = ss(varargin{:}); |
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191 |
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192 endfunction |
