Invariant Sets of Hybrid Autonomous Systems with Disturbance

<table>Trajectory of system <span class="svg-td" style="width: 121.475px;"><svg height="13.1" id="M107" style="vertical-align:-2.8125pt" version="1.1" viewbox="0 0 121.475 13.1" width="121.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.1)">
<g transform="translate(72,-61.52)">
<text transform="matrix(1,0,0,-1,-65.97,64.37)">
<tspan style="font-size: 11.21px; " x="0" y="0">̇</tspan>
<tspan style="font-size: 11.21px; " x="-5.9738641" y="0">𝑥</tspan>
<tspan style="font-size: 11.21px; " x="3.2951519" y="0">=</tspan>
<tspan style="font-size: 11.21px; " x="14.077248" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-45.66,61.57)">
<tspan style="font-size: 7.85px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-41.24,64.37)">
<tspan style="font-size: 11.21px; " x="0" y="0">(</tspan>
<tspan style="font-size: 11.21px; " x="3.732264" y="0">𝑥</tspan>
<tspan style="font-size: 11.21px; " x="9.8966637" y="0">)</tspan>
<tspan style="font-size: 11.21px; " x="13.628928" y="0">,</tspan>
<tspan style="font-size: 11.21px; " x="28.008793" y="0">̇</tspan>
<tspan style="font-size: 11.21px; " x="22.034927" y="0">𝑥</tspan>
<tspan style="font-size: 11.21px; " x="31.303944" y="0">=</tspan>
<tspan style="font-size: 11.21px; " x="42.097248" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,7.08,61.57)">
<tspan style="font-size: 7.85px; " x="0" y="0">2</tspan>
</text>
<text transform="matrix(1,0,0,-1,11.5,64.37)">
<tspan style="font-size: 11.21px; " x="0" y="0">(</tspan>
<tspan style="font-size: 11.21px; " x="3.732264" y="0">𝑥</tspan>
<tspan style="font-size: 11.21px; " x="9.8966637" y="0">)</tspan>
</text>
</g>
</g>
</svg></span>.</table>

Mathematical Problems in Engineering

Invariant Sets of Hybrid Autonomous Systems with Disturbance

Figure 3