Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

<table><svg height="14.6" id="M259" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 33.912498 14.6" width="33.912498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.9,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.02,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑘</tspan>
<tspan style="font-size: 12.50px; " x="10.940125" y="0">)</tspan>
</text>
</g>
</g>
</svg> (a) and time-varying delay, <svg height="13.45" id="M260" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 27.325001 13.45" width="27.325001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="6.6515961" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="10.815095" y="0">𝑘</tspan>
<tspan style="font-size: 12.50px; " x="17.591721" y="0">)</tspan>
</text>
</g>
</g>
</svg> (b).</table>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach 