# CME6.1 - Answer a System is asymptotically stable pm1 =...

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Sheet1 Page 1 %------------------------------------------------------ % CME 6.1a Lyapunov analysis %------------------------------------------------------ A = [-1 0 B = [1 C = [1 -(sqrt(2)/2)] D = [0] CharPoly = poly(A) % characteristic polynomial Poles = roots(CharPoly) % Find the system poles Q = eye(2) % matrix P = lyap(A',Q) pm1 = det(P(1,1)) %P is positive definite pm2 = det(P(1:2,1:2)) if (pm1>0 & pm2>0) % Logic to assess stability % condition disp('System is asymptotically stable.') else disp('System is unstable.') end EigsO = eig(A) % system eigenvalues

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Unformatted text preview: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Answer %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% a) System is asymptotically stable. pm1 = 0.500 pm2 = 0.125 EigsO = Since the real parts of the eignevalues are stirictly negative, this open-loop system is asymptotically stable. Sheet1 Page 2 0 -2] % Define the state-space realization sqrt(2)] % Determine the system % Given positive definite % Solve for P % Sylvester's method to see if % Calculate open-loop...
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