The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and n...The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.展开更多
Cross section production is one of the observable quantities in the hadronic systems. Inclusive cross section production J/ψ may be calculated through the use of the fragmentation c → J/ψ. In this paper we calculat...Cross section production is one of the observable quantities in the hadronic systems. Inclusive cross section production J/ψ may be calculated through the use of the fragmentation c → J/ψ. In this paper we calculate the inclusive cross section production J/ψ about the pole of Z^0 in the e^+e^- annihilation, through the lowest order regim of perturbative of QCD ananlyticaly. The obtained results arrive an excellent agreement with the exprimental data to produce the inclusive cross section production c → J/ψ.展开更多
基金Shanghai Science and Technology Devel-opm ent Funds ( No.0 1160 70 3 3)
文摘The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.
文摘Cross section production is one of the observable quantities in the hadronic systems. Inclusive cross section production J/ψ may be calculated through the use of the fragmentation c → J/ψ. In this paper we calculate the inclusive cross section production J/ψ about the pole of Z^0 in the e^+e^- annihilation, through the lowest order regim of perturbative of QCD ananlyticaly. The obtained results arrive an excellent agreement with the exprimental data to produce the inclusive cross section production c → J/ψ.
