Consensus of Noisy Multiagent Systems with Markovian Switching Topologies and Time-Varying Delays

<div>Probability of reaching consensus for multiagent system (<a href="https://static.hindawi.com/articles/mpe/volume-2015/453072/figures/#EEq1">1</a>) as a function of <svg height="10.2124pt" id="M567" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="593" vert-adv-y="593"></glyph.data></g></svg> over Markovian switching random graphs <svg height="12.7178pt" id="M568" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 43.0561 12.7178" width="43.0561pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M417 653C377 677 335 687 290 687C171 687 83 622 83 541C83 462 150 415 250 398C231 363 224 320 224 292C224 212 282 165 361 165C409 165 455 180 499 209L500 208C439 89 369 16 246 16C183 16 127 48 122 79H124C131 68 141 66 153 66C181 66 197 90 197 117C197 142 173 164 146 164C111 164 87 134 87 95C87 39 157 -15 256 -15C421 -15 531 60 586 209C606 264 620 298 652 330L637 346C520 239 440 195 368 195C324 195 302 225 302 262C302 293 311 343 343 390C542 390 740 489 740 593C740 642 693 669 637 669C526 669 359 580 263 428C175 440 124 482 124 541C124 602 193 657 297 657C332 657 369 652 408 635L417 653ZM699 590C699 512 532 420 361 420C425 535 557 632 642 632C673 632 699 618 699 590Z" id="g198-8"></path><glyph.data ascent="687" descent="-226" horiz-adv-x="773" vert-adv-y="773"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.049,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.547,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,25.457,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" id="g113-45"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.6,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="593" vert-adv-y="593"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,38.31,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg>.</div>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Consensus of Noisy Multiagent Systems with Markovian Switching Topologies and Time-Varying Delays 