Question

# A second order system starts with an initial condition of [23] without any external input. The state transition matrix for the system is given by [e−2t00e−t]. The state of the system at the end of 1 second is given by

A
[0.2711.100]
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B
[0.1350.368]
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C
[0.2710.736]
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D
[0.1351.100]
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Solution

## The correct option is A [0.2711.100] State transition matrix, ϕ(t)=[e−2t00e−t] Initial conditions, x(0)=[23] Zero input response is given by x(t)=ϕ(t)x(0) =[e−2t00e−t][23]=[2e−3t3e−1] State of the system at t=1s x(t)|t=1[2e−23e−1]=[0.2711.100]

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