Low Conservative Criteria for Robust Consensus of Multiagent Systems with Delays, Disturbances, and Topologies Uncertainties

<table>Jointly connected topologies <svg height="16.025" id="M171" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 45.962502 16.025" width="45.962502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.737)"><path d="M417 653l-9 -18q-48 22 -111 22q-76 0 -125 -34q-48 -35 -48 -82q0 -44 37 -74t102 -39q68 109 177 175q108 66 197 66q45 0 74 -20.5t29 -55.5q0 -50 -58 -98q-59 -48 -150 -76q-93 -29 -189 -29q-41 -61 -41 -128q0 -30 17.5 -48.5t48.5 -18.5q104 0 269 151l15 -16
q-35 -35 -66 -121q-83 -224 -330 -224q-72 0 -121 33q-48 34 -48 77q0 30 16.5 49.5t42.5 19.5q20 0 35.5 -14t15.5 -33q0 -22 -12 -36.5t-32 -14.5q-22 0 -29 13h-2q5 -24 41 -44q37 -19 83 -19q84 0 143 46.5t111 145.5l-1 1q-67 -44 -138 -44q-61 0 -99 35t-38 92
q0 54 26 106q-79 13 -123 50t-44 93q0 61 59 103q58 43 148 43q71 0 127 -34zM699 590q0 20 -16 31t-41 11q-66 0 -149 -64q-84 -63 -132 -148q81 0 162 26q80 26 128 65.5t48 78.5z" id="x1D4A2"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.2,15.825)"><path d="M483 97q-42 -50 -88.5 -79.5t-68.5 -29.5q-37 0 -17 93l22 102h-2q-54 -79 -144 -149q-59 -46 -100 -46q-24 0 -43 29t-19 86q0 78 34.5 153t94.5 120q41 31 94 51.5t98 20.5q29 0 72 -9q26 -6 39 -6l2 -4q-30 -117 -67 -323q-8 -41 2 -41q16 0 79 58zM374 387
q-32 15 -73 15q-52 0 -83 -23q-48 -36 -78 -108.5t-30 -152.5q0 -33 8.5 -50.5t20.5 -17.5q31 0 107 79t99 132q15 40 29 126z" id="x1D44E"></path></g>
<g transform="matrix(.017,-0,0,-.017,19.85,11.737)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,26.548,11.737)"><path d="M417 653l-9 -18q-48 22 -111 22q-76 0 -125 -34q-48 -35 -48 -82q0 -44 37 -74t102 -39q68 109 177 175q108 66 197 66q45 0 74 -20.5t29 -55.5q0 -50 -58 -98q-59 -48 -150 -76q-93 -29 -189 -29q-41 -61 -41 -128q0 -30 17.5 -48.5t48.5 -18.5q104 0 269 151l15 -16
q-35 -35 -66 -121q-83 -224 -330 -224q-72 0 -121 33q-48 34 -48 77q0 30 16.5 49.5t42.5 19.5q20 0 35.5 -14t15.5 -33q0 -22 -12 -36.5t-32 -14.5q-22 0 -29 13h-2q5 -24 41 -44q37 -19 83 -19q84 0 143 46.5t111 145.5l-1 1q-67 -44 -138 -44q-61 0 -99 35t-38 92
q0 54 26 106q-79 13 -123 50t-44 93q0 61 59 103q58 43 148 43q71 0 127 -34zM699 590q0 20 -16 31t-41 11q-66 0 -149 -64q-84 -63 -132 -148q81 0 162 26q80 26 128 65.5t48 78.5z" id="x1D4A2"></path></g>
<g transform="matrix(.012,-0,0,-.012,39.7,15.825)"><path d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76
q-31 0 -93.5 -49t-107.5 -110q-12 -37 -17 -70q-9 -65 12 -96.5t59 -31.5q31 0 56 14q53 29 89.5 105t36.5 162z" id="x1D44F"></path></g>
</svg> and <svg height="16.025" id="M172" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 45.799999 16.025" width="45.799999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.737)"><path d="M417 653l-9 -18q-48 22 -111 22q-76 0 -125 -34q-48 -35 -48 -82q0 -44 37 -74t102 -39q68 109 177 175q108 66 197 66q45 0 74 -20.5t29 -55.5q0 -50 -58 -98q-59 -48 -150 -76q-93 -29 -189 -29q-41 -61 -41 -128q0 -30 17.5 -48.5t48.5 -18.5q104 0 269 151l15 -16
q-35 -35 -66 -121q-83 -224 -330 -224q-72 0 -121 33q-48 34 -48 77q0 30 16.5 49.5t42.5 19.5q20 0 35.5 -14t15.5 -33q0 -22 -12 -36.5t-32 -14.5q-22 0 -29 13h-2q5 -24 41 -44q37 -19 83 -19q84 0 143 46.5t111 145.5l-1 1q-67 -44 -138 -44q-61 0 -99 35t-38 92
q0 54 26 106q-79 13 -123 50t-44 93q0 61 59 103q58 43 148 43q71 0 127 -34zM699 590q0 20 -16 31t-41 11q-66 0 -149 -64q-84 -63 -132 -148q81 0 162 26q80 26 128 65.5t48 78.5z" id="x1D4A2"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.2,15.825)"><path d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" id="x1D450"></path></g>
<g transform="matrix(.017,-0,0,-.017,18.65,11.737)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,25.365,11.737)"><path d="M417 653l-9 -18q-48 22 -111 22q-76 0 -125 -34q-48 -35 -48 -82q0 -44 37 -74t102 -39q68 109 177 175q108 66 197 66q45 0 74 -20.5t29 -55.5q0 -50 -58 -98q-59 -48 -150 -76q-93 -29 -189 -29q-41 -61 -41 -128q0 -30 17.5 -48.5t48.5 -18.5q104 0 269 151l15 -16
q-35 -35 -66 -121q-83 -224 -330 -224q-72 0 -121 33q-48 34 -48 77q0 30 16.5 49.5t42.5 19.5q20 0 35.5 -14t15.5 -33q0 -22 -12 -36.5t-32 -14.5q-22 0 -29 13h-2q5 -24 41 -44q37 -19 83 -19q84 0 143 46.5t111 145.5l-1 1q-67 -44 -138 -44q-61 0 -99 35t-38 92
q0 54 26 106q-79 13 -123 50t-44 93q0 61 59 103q58 43 148 43q71 0 127 -34zM699 590q0 20 -16 31t-41 11q-66 0 -149 -64q-84 -63 -132 -148q81 0 162 26q80 26 128 65.5t48 78.5z" id="x1D4A2"></path></g>
<g transform="matrix(.012,-0,0,-.012,38.5,15.825)"><path d="M530 686q-79 -330 -126 -595q-5 -24 4 -24q22 0 77 53l16 -24q-42 -49 -88 -78.5t-72 -29.5q-37 0 -19 83l21 99h-2q-62 -83 -153 -141q-65 -41 -97 -41q-28 0 -48 31.5t-20 91.5q0 71 32.5 144t88.5 118q36 30 94 52.5t94 22.5q38 0 68 -13l29 158q7 40 2 47.5t-38 7.5
h-35l1 26q39 4 76 13.5t58.5 17t27.5 7.5q16 0 9 -26zM387 375q-11 11 -38.5 20t-51.5 9q-45 0 -79 -23q-46 -32 -77.5 -107.5t-31.5 -143.5q0 -40 9.5 -58.5t23.5 -18.5q40 0 113.5 70t99.5 118z" id="x1D451"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Low Conservative Criteria for Robust Consensus of Multiagent Systems with Delays, Disturbances, and Topologies Uncertainties 