LEADER 03045nam 2200517 450 001 9910816872403321 005 20210618083341.0 010 $a1-119-68681-4 010 $a1-119-68684-9 010 $a1-119-68685-7 035 $a(CKB)4100000010013920 035 $a(MiAaPQ)EBC6001237 035 $a(CaSebORM)9781786304551 035 $a(EXLCZ)994100000010013920 100 $a20200228h20202019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis, modeling and stability of fractional order differential systems 2 $ethe infinite state approach /$fJean-Claude Trigeassou, Nezha Maamri 205 $a1st edition 210 1$aLondon :$cISTE Limited$d[2019] 210 4$dİ2019 215 $a1 online resource (409 pages) $cillustrations 225 1 $aSystems and industrial engineering series 311 $a1-78630-455-4 320 $aIncludes bibliographical references and index. 330 $aThis book introduces an original fractional calculus methodology ('the infinite state approach') which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation. With this approach, fundamental issues such as system state interpretation and system initialization ? long considered to be major theoretical pitfalls ? have been solved easily. Although originally introduced for numerical simulation and identification of FDEs, this approach also provides original solutions to many problems such as the initial conditions of fractional derivatives, the uniqueness of FDS transients, formulation of analytical transients, fractional differentiation of functions, state observation and control, definition of fractional energy, and Lyapunov stability analysis of linear and nonlinear fractional order systems. This second volume focuses on the initialization, observation and control of the distributed state, followed by stability analysis of fractional differential systems. 410 0$aSystems and industrial engineering series. 606 $aFractional calculus 606 $aFractional differential equations 606 $aFractional integrals 615 0$aFractional calculus. 615 0$aFractional differential equations. 615 0$aFractional integrals. 676 $a515.83 700 $aTrigeassou$b Jean-Claude$0880053 702 $aMaamri$b Nezha 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816872403321 996 $aAnalysis, modeling and stability of fractional order differential systems 2$94037360 997 $aUNINA