Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/mpe/volume-2017/3146231/figures/3146231.fig.002a.svgz" name="3146231.fig.002a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Sliding variable <svg height="16.9195pt" id="M233" style="vertical-align:-5.1323pt" version="1.1" viewbox="-0.0498162 -11.7872 70.8612 16.9195" width="70.8612pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path></g><g transform="matrix(.013,0,0,-0.013,10.979,0)"><path d="M535 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data="https://static.hindawi.com/articles/mpe/volume-2017/3146231/figures/3146231.fig.002c.svgz" name="3146231.fig.002c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Nominal control <svg height="9.25202pt" id="M236" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 12.001 9.25202" width="12.001pt" 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="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 96Z" id="g113-118"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.929,3.132)"><path d="M245 635C92 635 37 457 37 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<div>Simulation results. Finite-time state feedback control of a dynamic system subject to Hölder-type disturbances.</div>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes 