Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects

<table class="fixed-width table-group" id="tab1"><tr><td><table class="table"><colgroup><col style="width:4.83em"/><col style="width:6.30em"/><col style="width:7.39em"/><col style="width:11.05em"/><col style="width:5.75em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Methods</td><td class="align_center">Our method</td><td class="align_center">Pu and Tan [<a href="/journals/mpe/2018/3841675/#B1" target="_blank">1</a>]</td><td class="align_center">Xing-cheng and Wei [<a href="/journals/mpe/2018/3841675/#B15" target="_blank">15</a>]</td><td class="align_center">Li et al. [<a href="/journals/mpe/2018/3841675/#B26" target="_blank">26</a>]</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left"><span style="width: 6.40217ptpx;"><svg height="6.1673pt" id="M289" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.40217 6.1673" width="6.40217pt" 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="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path></g></svg></span></td><td class="align_center"><span style="width: 21.8649ptpx;"><svg height="8.55521pt" id="M290" style="vertical-align:-0.2063904pt" version="1.1" 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613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,15.444,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" 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<div>Maximum allowed <span class="nowrap"><svg height="6.1673pt" id="M288" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.40217 6.1673" width="6.40217pt" 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="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Stability of Stochastic Differential Switching Systems with Time-Delay and Impulsive Effects 