# Linear Systems and State Space Matrices

I need some help with these questions:

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.

https://brainmass.com/engineering/electrical-engineering/linear-systems-state-space-matrices-61675

#### Solution Summary

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.

Linear Systems and Linearized State Space

1. a) A system has the following model:

x_1 = x_2

x_2 = (-x_2)92+cos(x_1))-3sin(x_1 - u)

y = tan(x_1 - u)

Find the linearized state space model about the steady state with x = (0,0)^T.

b) Draw a Simulink implementation diagram of the system in question a. The input comes from a function generator and the output and simulation time must be sent to the workspace.

2. b) Find the natural response of the system (see attached), with input u(t) = 0 and initial condition x(0) = (-1,1)^T. Sketch your solution.

bii) Use the Laplace transform to find the output of the system (see attached), y = (0 1)x,

with x_0 = (1 0)^T and ut) = e^-3t.

bii) Sketch the solution and confirm that it makes sense.

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