Page 693 - Mathematical Techniques of Fractional Order Systems

Index 665

stabilization of, 294 295 Continuous-time fractional order chaotic
phase portrait of the imaginary part of, 287f systems, 409
phase portrait of the real part of, 287f biomedical applications, 429 432
terminal sliding mode control law for, 292 evaluation of arteriovenous stenosis in
Chen fractional order system, 319 321 hemodialysis patients, 429 431
Chen hyperchaotic system generalized chaotic susceptible infected
fractional order, 362 363 recovered epidemic model, 431 432
phase portraits of, 363f communications and encryption, 423 429
Chen system, 425 427 image encryption, 428 429
Chen Lee system, 429 430 substitution boxes, 427 428
Chuas fractional order circuit, 319 321, two-channel secure communication,
561 562 423 427
Circuit realization of fractional order control techniques, 415 418
hyperchaotic system, 284 sliding mode control, 415 417
Closed graph operator, 189 synchronization, 418 423
Combination Index (CI), 14 15 FPGA implementations, 436 439
Combined direct and indirect adaptive control, Gru ¨nwald Letnikov based FPGA
159 160 implementation of FOCS, 438 439
Commensurate fractional order permanent HDL coder-based implementation of
magnet synchronous motor model, FOCS, 437 438
531 532, 543 555 motors, 432 436
Commensurate order systems, 566 brushless DC Motor, 433 435
Communications and encryption, 423 429 permanent magnet synchronous motor,
image encryption, 428 429 436
substitution boxes, 427 428 simulation of fractional order chaotic
two-channel secure communication, systems, 413 415
423 427 Continuous-time LTI strictly-proper rational
Compact biochemical bone remodeling order system, 77
models, creating, 23 31 Continuous-time systems, 159, 412 413
Compact interval, 189 Control action (CA), 15
Complete desynchronization, 420 Control structure, basic block diagram of, 257f
Complete synchronization, 419, 626 627, 640 Control systems, direct/analytic synthesis of,
achieving, 325 96
multiswitching, 330 339 Controllability Grammian matrix, 246 247
Completely continuous multivalued map, 189, Controllability of dynamical systems, 229
233 234 Controllability of fractional higher order
Complex chaotic systems, nonidentical stochastic integrodifferential
synchronization of, 298 299 inclusions, 229
Complex hyperchaotic system discussion, 246
phase portrait for the imaginary part of, main results, 235 246
290f preliminaries, 231 235
phase portrait for the real part of, 289f Controllability results
Conservative hidden attractor with no of single-valued and multivalued FSDEs by
equilibria and quadratic nonlinearities, using (a, k)-regularized families of
517 bounded linear operators, 187 208
Continued fraction expansion (CFE), multivalued fractional stochastic integro-
437 438 differential equation, 187 201
Continuous operator, 242 solvability and optimal control results for
Continuously differentiable functions, FSDEs, 202 208
229 230 of single-valued fractional stochastic
Continuous-time chaotic systems, 412 413, differential equation by using analytic
626 627 resolvent operators, 208 225