Page 703 - Mathematical Techniques of Fractional Order Systems

Index 675

existence of mild solution, 212 222 Stability conditions, 81 85
existence of optimal control, 222 225 Stability of FOS, 326, 326f
preliminaries, 209 225 Stability of fractional order systems, 163, 326
Sliding mode control, 415 417, 603 607, Stabilization, 294 297
626 627 of fractional order complex Chen chaotic
Sliding mode controller (SMC), 249 250, system, 294 295
257 258, 260, 264, 276, 285 of fractional order complex Lorenz
design and implementation of, 257 hyperchaotic system, 296 297
Sliding mode stabilization and Stabilization, controller design for, 570 574,
synchronization, 283 576 579
chaotic and hyperchaotic systems, adaptive Steady-state response, 80
terminal sliding mode synchronization Stochastic differential equations (SDEs), 185
for, 292 294 Stochastic differential inclusions, 230, 247
discussion, 301 304 Stochastic Fubini theorem, 201
numerical simulation examples, 294 301 Stochastic system, 234
identical synchronization of fractional Strongly continuous family, 190
order complex hyperchaotic systems, Strongly continuous one-parameter family of
299 301 semigroup, 186
nonidentical synchronization of complex Sturm algorithm, 82
chaotic systems, 298 299 Sturm Liouville problems, 41 43
stabilization of the fractional order Substitution boxes (S-Boxes), 427 428
complex Chen chaotic system, Synchronization, 298 301, 349, 418 423,
294 295 453, 483 485, 625 626
stabilization of the fractional order of chaos, 319 321
complex Lorenz hyperchaotic system, of chaotic systems, 283 284
296 297 controller design for, 574 576
problem formulation, 286 289 of electrically coupled neuron systems,
chaotic and hyperchaotic systems, 421 422
286 289 of fractional order chaotic systems,
fractional order calculus preliminaries, 626 627
286 of fractional order modified Van der Pol-
terminal sliding mode control law Duffing circuit, 420 421
for Chen chaotic system, 292 identical synchronization of fractional order
for Lorenz hyperchaotic system, 292 complex hyperchaotic systems,
Sliding surface, 605 299 301
Small diagonal segments, 630 nonidentical synchronization of complex
Solvability and optimal control results for chaotic systems, 298 299
FSDEs, 202 208 sliding mode synchronization of uncertain
existence of mild solution, 204 206 chaotic systems, 422 423
existence of optimal control result, types of, 452, 626 627
206 208 using active backstepping, 579 581
preliminaries, 202 204
Spectral homotopy analysis method (SHAM),
41 43 T
Spline method, 58 60 Taylor theorem, 40
S-system, 16 Tent map with shaping parameters, 386 387
Stability analysis, 125 129 Terminal sliding mode control law
in presence of time-varying delays, for Chen chaotic system, 292
138 147 for Lorenz hyperchaotic system, 292
time-delay-dependent stability, 143 147 Texture, 629
time-delay-independent stability, Theory of chaos, 625, 628
139 143 Theory of fractional order systems, 75