A control system is described by and 20-[3] -0+ [1] -0. u(t), y(t) = [10] x(t), where u, a, and y are the input, the state, and the output variables, respectively. a) Determine whether or not the sytem is stable in the state-sense. Show your work clearly. b) Find the state transion matrix for the systm.)! c) Determine x(t) for t≥ 0, when x(0) = [1 0], and u(t) = 1 for t≥ 0. Show all your work clearly.

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A control system is described by
and
200-[-0+[1] -0.
u(t),
de(t) =
y(t) = [ 10 ] æ(t),
where u, a, and y are the input, the state, and the output variables, respectively.
a) Determine whether or not the sytem is stable in the state-sense. Show your work
clearly.
b) Find the state transion matrix for the systm.)
c) Determine x(t) for t≥ 0, when x(0) = [1 0], and u(t) = 1 for t≥ 0. Show all your work
clearly.
Transcribed Image Text:A control system is described by and 200-[-0+[1] -0. u(t), de(t) = y(t) = [ 10 ] æ(t), where u, a, and y are the input, the state, and the output variables, respectively. a) Determine whether or not the sytem is stable in the state-sense. Show your work clearly. b) Find the state transion matrix for the systm.) c) Determine x(t) for t≥ 0, when x(0) = [1 0], and u(t) = 1 for t≥ 0. Show all your work clearly.
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