iii. The block diagram of a Linear Quadratic Regulator (LQR) is shown in Figure 2. r=0 + X x = Ax+Bu C K Figure 2: Linear Quadratic Regulator If the state equation of the plant is; 0 - 20-4- + []u And the performance index J is given as; 10 J = [ {x [0] x + 0.2 u}dt 0 Find. a. The Riccati matrix P. (Note that P is a positive symmetric matri solutionspile.com

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iii. The block diagram of a Linear Quadratic Regulator (LQR) is shown in Figure 2. r=0 + X x = Ax+Bu C K Figure 2: Linear Quadratic Regulator If the state equation of the plant is; 0 - 20-4- + []u And the performance index J is given as; 10 J = [ {x [0] x + 0.2 u}dt 0 Find. a. The Riccati matrix P. (Note that P is a positive symmetric matrix) b. The state feedback matrix K c. The closed-loop eigenvalues d. Discuss the stability of the system. [16 Marks] [Total 25 Marks] solutionspile.com

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(Solved): iii. The block diagram of a Linear Quadratic Regulator (LQR) is shown in Figure 2. r=0 + X x = Ax+ ...

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