# Averaging, integral of special function

## Homework Statement

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

$$\dot{x_1} = x_2$$
$$\dot{x_2} = -x_1 + 1 -2u(0.5sat(x_2) + 0.5 - p(t))$$

## Homework Equations

u(s) = 0 for s<0, u(s) = 1 for s>=0
p(t) is periodic with T = 1
$$f_{avg} =\frac{1}{T}\int_0^Tf(x,t)$$

## The Attempt at a Solution

$$\dot{x_1} = x_2$$
$$\dot{x_2} = -x1 - sat(x_2)$$

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