Preservation of Stability and Synchronization of a Class of Fractional-Order Systems

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="928930.fig.003a" src="https://static-preview.hindawi.com/articles/mpe/volume-2012/928930/figures/928930.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b> Synchronization error of the systems without modification</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="928930.fig.003b" src="https://static-preview.hindawi.com/articles/mpe/volume-2012/928930/figures/928930.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b> Synchronization error of the modified systems</td></tr></table></td></tr></table>

<table>Errors graph with the control law applied at <svg height="11.125" id="M352" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 50.737499 11.125" width="50.737499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,10.863)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g><g transform="matrix(.017,0,0,-.017,10.568,10.863)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,0,0,-.017,25.272,10.863)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,0,0,-.017,33.431,10.863)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
l-26 -65h-233z" id="x35"></path></g><g transform="matrix(.017,0,0,-.017,44.429,10.863)"><path d="M319 325l-25 -7q-33 99 -103 99q-29 0 -47 -19.5t-18 -49.5t22 -49.5t62 -36.5q63 -26 95 -57t32 -79q0 -64 -50 -101t-115 -37q-35 0 -67.5 10.5t-46.5 23.5q-5 11 -11 51t-6 67l27 5q14 -53 46.5 -88.5t75.5 -35.5q29 0 50 19.5t21 50.5t-19.5 51.5t-59.5 39.5
q-28 12 -46 22.5t-38.5 27t-30.5 38.5t-10 49q0 54 42.5 92t109.5 38q48 0 88 -18q6 -15 13 -50.5t9 -55.5z" id="x73"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Preservation of Stability and Synchronization of a Class of Fractional-Order Systems 