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Linear Systems and State Space Matrices

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2. Calculate the linear state space matrices A,B,C and D for system that is described by the state equations, for deviations from uop = [-1, 1]^T, xop = [1,1,0]^T and yop= [0] (see attached file for better formula representation).

3. A linear system is described by its transfer function T(s) = s-1/ s^2 + 6s+ 5
- Derive the time-domain expression for the unit step response of this system
- Sketch the unit step response of this system over 3 times the longer of the two time constraints.

4. A linear system is described by its transfer function T(2) = (18+59.1s-3s^2)/(s^2+0.3s+9)(20+s)
- Draw the Bode magnitude and phase angle plots of T(iw) on the attached EdS graph paper for 0.03<w<30
- Transfer the frequency response from the Bode plot to the adjacent logarithmic complex plane. Mark w=0.1, 0.4, 3, and 10 on the frequency response.

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This in-depth solution shows step-by-step calculations to determine concepts of linear state space matrices, unit step response of the system, time-domain expression, logarithmic complex plane and other variables of a linear system.

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