6. Consider the following system 3 0 1] [1] -3 1 0x+0u 1 0 0 y...

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6. Consider the following system 3 0 1] [1] -3 1 0x+0u 1 0 0 y = Cx+[0]u dx dt a) Determine if the system is observable for the following values of C. C [101], C [010], C = [001] b) For the system with C, rewrite the system in observable canonical form. Use this result to find the transformation T, necessary to put the system in observable canonical form. c) For the system with Cz, consider the linear observer (A-LC) where L=[1 1 1]. Does this produce a valid observe for the system? Be sure to explain your answer. d) Design a linear observer that asymptotically converges to the true trajectory, i.e. so that the error ( e = x - ) goes to zero. 6. Consider the following system 3 0 1] [1] -3 1 0x+0u 1 0 0 y = Cx+[0]u dx dt a) Determine if the system is observable for the following values of C. C [101], C [010], C = [001] b) For the system with C, rewrite the system in observable canonical form. Use this result to find the transformation T, necessary to put the system in observable canonical form. c) For the system with Cz, consider the linear observer (A-LC) where L=[1 1 1]. Does this produce a valid observe for the system? Be sure to explain your answer. d) Design a linear observer that asymptotically converges to the true trajectory, i.e. so that the error ( e = x - ) goes to zero.