An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at...An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.展开更多
The state space representations of fractional order linear time- invariant（LTI） systems are introduced, and their solution formulas are deduced hy means of Laplace transform. The stability condition of fractional or...The state space representations of fractional order linear time- invariant（LTI） systems are introduced, and their solution formulas are deduced hy means of Laplace transform. The stability condition of fractional order LTI systems is given, and its proof is deduced by means of using linear non - singularity transform and the derivative property of Mittag-Leffler function. The controllability condition of fractional m＇der LTI systems is given, and its proof is deduced by means of using its characteristic polynomial and the Cayley-Hamilton theorem. The observability condition of fractional order LTI systems is given, and its proof is deduced by means of their solution formulas. Finally an example is given to prove the correctness of the stability, controllability, and observability conditions mentioned above, s are deduced by means of Laplace transform. Their stability, controllability and observability conditions are given as well as their proofs.展开更多
基金Sponsored by 863 Project (Grant No.2002AA517020) Developing Fund of Shanghai Science Committee (Grant No.011607033).
文摘An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.
基金stability, coSponsored by the National High Technology Research and Development Program of China (Grant No.2003AA517020), the National Natural Science Foundation of China (Grant No.50206012), and Developing Fund of Shanghai Science Committee (Grant No.011607033).
文摘The state space representations of fractional order linear time- invariant（LTI） systems are introduced, and their solution formulas are deduced hy means of Laplace transform. The stability condition of fractional order LTI systems is given, and its proof is deduced by means of using linear non - singularity transform and the derivative property of Mittag-Leffler function. The controllability condition of fractional m＇der LTI systems is given, and its proof is deduced by means of using its characteristic polynomial and the Cayley-Hamilton theorem. The observability condition of fractional order LTI systems is given, and its proof is deduced by means of their solution formulas. Finally an example is given to prove the correctness of the stability, controllability, and observability conditions mentioned above, s are deduced by means of Laplace transform. Their stability, controllability and observability conditions are given as well as their proofs.
