IV. Asymmetric Riccati Equation (ARE): Let T TA-AT=A-TAT (nonlinear) a) Prove: Given the partitioned NxN matrix...

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IV. Asymmetric Riccati Equation (ARE): Let T TA-AT=A-TAT (nonlinear) a) Prove: Given the partitioned NxN matrix P= b) Let T satisfy ARE. Given the partitioned NxN matrix I 0 = A= [41 42 A2 A22. Prove: PAP= 0 A12 A22-TA This means: {eigenvalues of A} = {eigenvalues of A + AT} {eigenvalues of A2-TA} [0 1 1 c) Let A=000. Partition so that A = -2 and solve ARE for T 0 1 -2] d)Use b) & c) to solve for the eigenvalues of A. Check by finding them directly. IV. Asymmetric Riccati Equation (ARE): Let T TA-AT=A-TAT (nonlinear) a) Prove: Given the partitioned NxN matrix P= b) Let T satisfy ARE. Given the partitioned NxN matrix I 0 = A= [41 42 A2 A22. Prove: PAP= 0 A12 A22-TA This means: {eigenvalues of A} = {eigenvalues of A + AT} {eigenvalues of A2-TA} [0 1 1 c) Let A=000. Partition so that A = -2 and solve ARE for T 0 1 -2] d)Use b) & c) to solve for the eigenvalues of A. Check by finding them directly.