Impulsive Consensus for Leader-Following Multiagent Systems with Fixed and Switching Topology

<table>Trajectory of the multiagent system (<a href="https://static.hindawi.com/articles/mpe/volume-2013/762861/figures/#EEq2.2">2</a>) under fixed topology, when <svg height="15.8875" id="M350" style="vertical-align:-3.9858pt" version="1.1" viewbox="0 0 64.3125 15.8875" width="64.3125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>. Evolution of (a) <svg height="11.9625" id="M351" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 13.5 11.9625" width="13.5" 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)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
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<g transform="matrix(.012,-0,0,-.012,9.563,11.762)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
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</svg>, and (b) <svg height="11.925" id="M352" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 11.35 11.925" width="11.35" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.638)"><path d="M457 332q0 -81 -41 -161.5t-105.5 -131.5t-129.5 -51q-46 0 -79 30.5t-33 86.5q0 18 7 51q18 95 46 187q6 19 6 33q0 7 -7 7q-24 0 -78 -64l-20 23q32 48 73 77t78 29q33 0 33 -46q0 -38 -10 -70q-28 -92 -39 -152q-7 -38 -7 -57q0 -78 69 -78q68 0 118 75.5t50 194.5
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</svg>.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Impulsive Consensus for Leader-Following Multiagent Systems with Fixed and Switching Topology 