3.4.1 部分分数分解


 関数 "residue" による部分分数分解 ...... M ファイル ex_residue.m (p.56)
clear
format compact

numQ11 = [1 11];  numQ12 = 1;
numQ21 = -10;     numQ22 = [1 0];
denQ   = conv([1 10],[1 1]);

[k11, p] = residue(numQ11, denQ);
[k12, p] = residue(numQ12, denQ);
[k21, p] = residue(numQ21, denQ);
[k22, p] = residue(numQ22, denQ);
p

K1 = [ k11(1)  k12(1)
       k21(1)  k22(1) ]
K2 = [ k11(2)  k12(2)
       k21(2)  k22(2) ]
>> ex_residue
p =
   -10
    -1
K1 =
   -0.1111   -0.1111
    1.1111    1.1111
K2 =
    1.1111    0.1111
   -1.1111   -0.1111

 ヘビサイドの公式(数式処理) ...... M ファイル symb_frac.m (p.57)
clear
format compact

A = [  0   1
     -10 -11 ];
syms s

p = eig(A); p1 = p(2), p2 = p(1)
I = eye(2); 
Q = inv(s*I - A)
eq1 = simplify((s - p1)*Q);
eq2 = simplify((s - p2)*Q);

K1 = subs(eq1, s, p1)
K2 = subs(eq2, s, p2)
>> symb_frac
p1 =
   -10
p2 =
    -1
Q =
[ (s + 11)/(s^2 + 11*s + 10), 1/(s^2 + 11*s + 10)]
[      -10/(s^2 + 11*s + 10), s/(s^2 + 11*s + 10)]
K1 =
   -0.1111   -0.1111
    1.1111    1.1111
K2 =
    1.1111    0.1111
   -1.1111   -0.1111
>> sym(K1)
ans =
[ -1/9, -1/9]
[ 10/9, 10/9]
>> sym(K2)
ans =
[  10/9,  1/9]
[ -10/9, -1/9]