Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System

<table>Illustration of the partitioning of <svg height="9.8625002" id="M38" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.8625)">
<g transform="translate(72,-64.11)">
<text transform="matrix(1,0,0,-1,-71.95,66.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑦</tspan>
</text>
</g>
</g>
</svg> and <svg height="10.55" id="M39" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.55)">
<g transform="translate(72,-63.56)">
<text transform="matrix(1,0,0,-1,-71.95,63.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐴</tspan>
</text>
</g>
</g>
</svg> for <svg height="12.8875" id="M40" style="vertical-align:-1.76814pt" version="1.1" viewbox="0 0 52.75 12.8875" width="52.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.8875)">
<g transform="translate(72,-61.69)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
<tspan style="font-size: 12.50px; " x="12.340461" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="24.38085" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="30.632351" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="35.8461" y="0">2</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System 