Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator

<div>Communication graphs. Left: undirected graph <span class="nowrap"><svg height="12.3524pt" id="M289" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -9.1709 15.9287 12.3524" width="15.9287pt" 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="M422 682C387 695 357 699 317 699C181 699 82 633 82 548C82 472 149 424 253 401C233 362 226 321 226 296C226 212 296 162 389 162C421 162 463 169 491 181L493 179C436 80 364 34 264 34C219 34 189 50 178 65V66C218 73 236 105 236 134C236 169 211 201 167 201C120 201 84 158 84 108C84 32 155 -21 272 -21C459 -21 585 56 641 209C664 269 678 309 707 336L668 368C537 250 498 217 406 217C371 217 360 244 360 279C360 318 375 364 390 391C485 394 576 415 649 448C738 488 799 543 799 602C799 662 746 687 665 687C543 687 382 600 284 457C220 472 173 496 173 548C173 609 232 644 324 644C347 644 380 642 408 634L422 682ZM424 447C488 548 589 632 665 632C696 632 708 617 708 593C708 519 576 454 424 446V447Z" id="g199-8"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.842,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg>.</span> Right: directed graph <span class="nowrap"><svg height="12.3524pt" id="M290" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -9.1709 15.9287 12.3524" width="15.9287pt" 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="M422 682C387 695 357 699 317 699C181 699 82 633 82 548C82 472 149 424 253 401C233 362 226 321 226 296C226 212 296 162 389 162C421 162 463 169 491 181L493 179C436 80 364 34 264 34C219 34 189 50 178 65V66C218 73 236 105 236 134C236 169 211 201 167 201C120 201 84 158 84 108C84 32 155 -21 272 -21C459 -21 585 56 641 209C664 269 678 309 707 336L668 368C537 250 498 217 406 217C371 217 360 244 360 279C360 318 375 364 390 391C485 394 576 415 649 448C738 488 799 543 799 602C799 662 746 687 665 687C543 687 382 600 284 457C220 472 173 496 173 548C173 609 232 644 324 644C347 644 380 642 408 634L422 682ZM424 447C488 548 589 632 665 632C696 632 708 617 708 593C708 519 576 454 424 446V447Z" id="g199-8"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.842,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator 