Begin with the system described by the following state-space equations: -7 2 + [3] u(1) *(t)...

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Begin with the system described by the following state-space equations: -7 2 + [3] u(1) *(t) = y(t) = [11] Given the input u(t) = 1, to = 0, t≥ to, x(0) = [1 -1], do the following 1. (50 pts.) First, work directly from Equations 1 and 2. Perform all work by hand unless otherwise instructed: x(t) + (t) + 3u(t) (1) (2) (a) Determine the transfer function of the system, g(s). (b) Determine the equation for the zero-state response of this system. (c) Plot the zero-state response equation from (b) in MATLAB over 0 ≤ t ≤ 5 seconds and include a labeled plot in your report. (d) Determine the equation for the zero-input response of this system. (e) Plot the zero-input response equation from (d) in MATLAB over 0 ≤ t ≤ 5 seconds and include a labeled plot in your report. (f) Determine the equation for the total response of this system. (g) Plot the total response equation from (f) in MATLAB over 0 ≤ t ≤ 5 seconds and include a labeled plot in your report. (h) Determine whether the system is controllable and/or observable by examining the controllability and observability matrices. (i) Determine the modal form of the system. If it is possible, from the modal form confirm your findings from (h) and determine whether the system is stabilizable or detectable. (j) Based on the eigenvalues of A, is this system stable? Why or why not? Begin with the system described by the following state-space equations: -7 2 + [3] u(1) *(t) = y(t) = [11] Given the input u(t) = 1, to = 0, t≥ to, x(0) = [1 -1], do the following 1. (50 pts.) First, work directly from Equations 1 and 2. Perform all work by hand unless otherwise instructed: x(t) + (t) + 3u(t) (1) (2) (a) Determine the transfer function of the system, g(s). (b) Determine the equation for the zero-state response of this system. (c) Plot the zero-state response equation from (b) in MATLAB over 0 ≤ t ≤ 5 seconds and include a labeled plot in your report. (d) Determine the equation for the zero-input response of this system. (e) Plot the zero-input response equation from (d) in MATLAB over 0 ≤ t ≤ 5 seconds and include a labeled plot in your report. (f) Determine the equation for the total response of this system. (g) Plot the total response equation from (f) in MATLAB over 0 ≤ t ≤ 5 seconds and include a labeled plot in your report. (h) Determine whether the system is controllable and/or observable by examining the controllability and observability matrices. (i) Determine the modal form of the system. If it is possible, from the modal form confirm your findings from (h) and determine whether the system is stabilizable or detectable. (j) Based on the eigenvalues of A, is this system stable? Why or why not?