i = Ar + Bu y=Cr + Du, where reR, ERP, and y ERP. (i) Suppose -1 0 -1 A= 0 -1 0 Lo 0-2 Ti 01 B = 0 1 Loo [100] 0 1 0 and (a) Find an invertible matrix P to diagonalize A such that P-1AP = A, where A is a diagonal matrix. This should be done by hand. (b) Compute At by hand. (c) Assume (0) = [0.1,0.2,0.3) and u(t) = (sin(t), cos(t))", + > 0. Plot r(t) and y(t) using Matlab (No hand computation is required). Attach your code (no need to email me the code). (d) is the system marginally or asymptotically stable? Why? Is the system BIBO stable? Why? Part (d) should be answered according to the results obtained from (a), (b), and (c). No further computation is allowed. i = Ar + Bu y=Cr + Du, where reR, ERP, and y ERP. (i) Suppose -1 0 -1 A= 0 -1 0 Lo 0-2 Ti 01 B = 0 1 Loo [100] 0 1 0 and (a) Find an invertible matrix P to diagonalize A such that P-1AP = A, where A is a diagonal matrix. This should be done by hand. (b) Compute At by hand. (c) Assume (0) = [0.1,0.2,0.3) and u(t) = (sin(t), cos(t))", + > 0. Plot r(t) and y(t) using Matlab (No hand computation is required). Attach your code (no need to email me the code). (d) is the system marginally or asymptotically stable? Why? Is the system BIBO stable? Why? Part (d) should be answered according to the results obtained from (a), (b), and (c). No further computation is allowed