In [1]:

    

import numpy as np
import sympy as sy


    

In [2]:

    

s,z = sy.symbols('s,z', real=False)
l_1, l_2 = sy.symbols('l1, l2')


    

In [3]:

    

Phi = sy.Matrix([[1.13, 0.52], [0.52, 1.13]])
Gamma = sy.Matrix([[0.13],[0.52]])
L = sy.Matrix([[l_1, l_2]])

M = z*sy.Matrix.eye(2) - (Phi - Gamma*L)
M


    

    
Out[3]:





Matrix([
[0.13*l1 + z - 1.13,     0.13*l2 - 0.52],
[    0.52*l1 - 0.52, 0.52*l2 + z - 1.13]])

In [6]:

    

chPoly = sy.poly(M.det(), z)
chPoly


    

    
Out[6]:





Poly(1.0*z**2 + (0.13*l1 + 0.52*l2 - 2.26)*z + 0.1235*l1 - 0.52*l2 + 1.0065, z, domain='RR[l1,l2]')

In [9]:

    

chDesired = sy.simplify(sy.expand((z-np.exp(-0.5))**2))

sol = sy.solve((chPoly - chDesired).coeffs(), [l_1, l_2])


    

In [10]:

    

sol


    

    
Out[10]:





{l1: 1.61072237375216, l2: 1.61066302305182}

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