Consider the system where Xk+1 = and A A = and b = (11). Compute the...
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Consider the system where Xk+1 = and A A = and b = (11). Compute the equivalent representation corresponding to a similarity transformation where the first vector of V is an eigenvector of A. Then use this representation to compute a matrix K := (k₁ ka) such that one of the eigenvalues of ABK is at 0.5. Can you change the other eigenvalue? This problem extends Problem 3. Consider the system Tk+1= Ak + buk, where x R³ and u R; thus A & R³x3 and b = R³×1, Let Axk+ Buk 0 1 1 2 b= 3.0750 8.0250 0.1500 1.0250 2.6750 0.5500 0.1500 1.0000 0.0500 = 5 1 Compute a gain matrix K = R¹x3 such that, with the feedback law defined by the equation E Uk = Kæk, the eigenvalues associated with the reachable modes are at 0.9 and 0.8. Consider the system where Xk+1 = and A A = and b = (11). Compute the equivalent representation corresponding to a similarity transformation where the first vector of V is an eigenvector of A. Then use this representation to compute a matrix K := (k₁ ka) such that one of the eigenvalues of ABK is at 0.5. Can you change the other eigenvalue? This problem extends Problem 3. Consider the system Tk+1= Ak + buk, where x R³ and u R; thus A & R³x3 and b = R³×1, Let Axk+ Buk 0 1 1 2 b= 3.0750 8.0250 0.1500 1.0250 2.6750 0.5500 0.1500 1.0000 0.0500 = 5 1 Compute a gain matrix K = R¹x3 such that, with the feedback law defined by the equation E Uk = Kæk, the eigenvalues associated with the reachable modes are at 0.9 and 0.8.
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