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Control Systems, State Space Form and Convolution Integrals

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A control system is represented in the state space form by the following equations in the attached file.

a) Solve for the state vector using the convolution integral
b) Find the output, y(t)

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Problem:

A control system is represented in the state space form by the following equations:

a) Solve for the state-transition matrix
b) Solve for the state vector using the convolution integral
c) Find the output y(t)

Solution:

a) For a simple linear differential equation with constant coefficients of form
, a = constant (1)
and with initial condition
(2)
the solution is given by
(3)
This formula can be written in another form, using the convolution integral:
(4)
where
...

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