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- close all;
- clear;
- clc;
- %% 1
- A = [0 1; 0 0]
- B = [0; 1]
- cT = [1 0]
- d = [0]
- A = [3 3; 2 0]
- B = [0 3; 3 -1]
- cT = [1 -2]
- d = [0 0]
- syms Ta
- % Euler
- Phi1 = eye(2) + A*Ta
- Gamma1 = B
- % exakt
- Phi2 = expm(A*Ta)
- %Phi2 = eye(2) + A*Ta + A^2*Ta^2/2
- Gamma2 = int(Phi2, Ta, 0, Ta)*B
- Ta = 1
- Phi1subbed = subs(Phi1)
- Gamma1subbed = subs(Gamma1)
- Phi2subbed = subs(Phi2)
- Gamma2subbed = subs(Gamma2)
- %% 2
- Phi3 = [-14 -90 7 -56; 10 84 -10 55; 0 -18 -7 -12; -14 -126 14 -83]
- Gamma3 = [3; -2; 1; 3]
- R = [Gamma3, Phi3*Gamma3, Phi3^2*Gamma3, Phi3^3*Gamma3, Phi3^4*Gamma3, Phi3^5*Gamma3]
- rank(R)
- Rred = R(:,1:rank(R))
- % x = l1 * v1 + l2 * v2
- % e^T_n = Gamma^T_R = v^T_1 * R
- PhiS = [0 1; -6 -7]
- GammaS = [0; 1]
- poles = roots([1 -3/10 1/50])
- -acker(PhiS, GammaS, poles)
- %% 3
- Phi4 = [9/8 -21/8 7/2; 13/8 7/8 1/2; -3/8 27/8 -13/4]
- Gamma4 = [5; -1; -5]
- cT2 = [1 -1 2]
- Phi4g = [0 1 0; 0 0 1; 0 0 0]
- syms k1 k2 k3
- kT = [k1 k2 k3]
- Gamma4 * kT
- Phi4g - Phi4
- % Phi4 + Gamma4 * kT = Phi4g
- kT = -acker(Phi4', cT2', [0 0 0])
- e = [1;1;1];
- for i=0:3000
- e = Phi4*e;
- end
- norm(e)
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