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## Homework Statement

Integrate the right hand side of the state equation to find the average system

[tex]\dot{x_1} = x_2[/tex]

[tex]\dot{x_2} = -x_1 + 1 -2u(0.5sat(x_2) + 0.5 - p(t))[/tex]

## Homework Equations

u(s) = 0 for s<0, u(s) = 1 for s>=0

p(t) is periodic with T = 1

[tex]f_{avg} =\frac{1}{T}\int_0^Tf(x,t)[/tex]

## The Attempt at a Solution

[tex]\dot{x_1} = x_2[/tex]

[tex]\dot{x_2} = -x1 - sat(x_2)[/tex]

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