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# HW2_3 - Ep = diag Ep(3,3 Ep(2,2 Ep(1,1 E Ap Qp Ep inv(Qp...

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% Linear Systems, Homework 3 % Date: 11/13/06 % File: HW2_3.m % Note: Algebraically Equivalence % Name: Feng-Li Lian, [email protected] % close all; clear all; c R = 1; L = 0.6; C1 = 1/6; C2 = 5/3; C % 1a % Ap = [ -1/(R*C1) 0 -1/C1; 0 0 1/C2; 1/L -1/L 0]; Bp = [ 1/(R*C1) ; 0 ; 0 ]; Cp = [ 0 1 0 ]; Dp = 0; D Sysp = ss(Ap,Bp,Cp,Dp); S % 1b % poly(Ap); p % 1c % [Nump, Denp] = ss2tf( Ap, Bp, Cp, Dp ); [ %2a % Ac = [ 0 1 0; 0 0 1; -6 -11 -6]; Bc = [ 0; 0; 6 ]; Cc = [ 1 0 0 ]; Dc = 0; D Sysc = ss(Ac,Bc,Cc,Dc); S % 2b % poly(Ac); p [Numc, Denc] = ss2tf( Ac, Bc, Cc, Dc ); [ % 2c % eig(Ap); eig(Ac); e T = [ 0 1 0; 0 0 0.6; 1 -1 0]; T

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T * Ap * inv(T); Ac; A T * Bp; Bc; B Cp * inv(T); Cc; % eigenvalue & eigenvector % [Qp,Ep]=eig(Ap); Qp = [ Qp(:,3) Qp(:,2) Qp(:,1) ]
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Unformatted text preview: Ep = diag( [ Ep(3,3), Ep(2,2), Ep(1,1)] ) E Ap Qp * Ep * inv(Qp) Q [Qc,Ec]=eig(Ac); Ac Qc * Ec * inv(Qc) Q [Qd,Ed]=eig(Ad); Ad Qd * Ed * inv(Qd) Q % transformation % T = [ 0 1 0; 0 0 0.6; 1 -1 0]; T T * Ap * inv(T) Ac A T * Bp Bc B Cp * inv(T) Cc % eigenvalue & eigenvector by null space calculation % q1 = [ -6/5; -3/5; 1 ]; q2 = [ -3/2; -3/10; 1]; q3 = [ -2; -1/5; 1 ]; q Q = [ q1 q2 q3 ]; Q Ad = inv(Q)*Ap*(Q) Td = inv(Q) T Bd = [ 3; -6; 3 ]; Cd = [ 1 1 1 ]; Dd = 0; D bigCp = [ Bp Ap*Bp Ap^2*Bp]; bigCc = [ Bc Ac*Bc Ac^2*Bc]; b T = bigCc*inv(bigCp) T T * Ap * inv(T) Ac A T * Bp Bc B Cp * inv(T) Cc C...
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