Robust Control for Systems with Bounded-Sensor Faults

<table>(Case no. 2): True sensor functions, <svg height="16.3125" id="M359" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 43.650002 16.3125" width="43.650002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.813)"><use xlink:href="#x1D719"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.663,15.888)"><use xlink:href="#x31"></use></g>
<g transform="matrix(.017,-0,0,-.017,20.725,11.813)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,35.412,11.813)"><use xlink:href="#x31"></use></g>
</svg> and <svg height="16.625" id="M360" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 155.875 16.625" width="155.875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x1D719"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.663,16.213)"><use xlink:href="#x32"></use></g>
<g transform="matrix(.017,-0,0,-.017,20.725,12.138)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,35.412,12.138)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,43.571,12.138)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,47.447,12.138)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,59.38,12.138)"><use xlink:href="#x2B"></use></g><g transform="matrix(.017,-0,0,-.017,73.149,12.138)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,81.309,12.138)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,85.184,12.138)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,96.165,12.138)"><use xlink:href="#x73"></use></g><g transform="matrix(.017,-0,0,-.017,102.404,12.138)"><use xlink:href="#x69"></use></g><g transform="matrix(.017,-0,0,-.017,106.96,12.138)"><use xlink:href="#x6E"></use></g><g transform="matrix(.017,-0,0,-.017,121.936,12.138)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,127.817,12.138)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,135.977,12.138)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,144.136,12.138)"><use xlink:href="#x1D461"></use></g><g transform="matrix(.017,-0,0,-.017,149.932,12.138)"><use xlink:href="#x29"></use></g>
</svg>, and estimated sensor functions, <svg height="20.85" id="M361" style="vertical-align:-4.24515pt" version="1.1" viewbox="0 0 16.0625 20.85" width="16.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.875,11.388)"><use xlink:href="#xF5C01"></use></g><g transform="matrix(.017,-0,0,-.017,.063,15.5)"><use xlink:href="#x1D719"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.663,20.788)"><use xlink:href="#x31"></use></g>
</svg> and <svg height="20.85" id="M362" style="vertical-align:-4.24515pt" version="1.1" viewbox="0 0 16.0625 20.85" width="16.0625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.875,11.388)"><use xlink:href="#xF5C01"></use></g><g transform="matrix(.017,-0,0,-.017,.063,15.5)"><use xlink:href="#x1D719"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.663,20.788)"><use xlink:href="#x32"></use></g>
</svg>, for <svg height="16.4375" id="M363" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 65.3125 16.4375" width="65.3125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.95)"><use xlink:href="#x1D719"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.663,16.025)"><use xlink:href="#x32"></use></g>
<g transform="matrix(.017,-0,0,-.017,20.725,11.95)"><use xlink:href="#x2209"></use></g><g transform="matrix(.017,-0,0,-.017,34.409,11.95)"><use xlink:href="#x1D4D1"></use></g><g transform="matrix(.017,-0,0,-.017,52.428,11.95)"><use xlink:href="#x3A6"></use></g>
</svg>. The control input, <svg height="7.9499998" id="M364" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.2749996 7.9499998" width="9.2749996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D462"></use></g>
</svg>, is also shown.</table>

Mathematical Problems in Engineering

Robust Control for Systems with Bounded-Sensor Faults

Figure 6