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In this study, fractional order indirect model reference adaptive control method is used to control a class of fractional order systems. Unlike the traditional integer order case, the controller is obtained by Lyapunov method and the closed-loop stability is achieved via indirect Lyapunov method rather than the certainty equivalence principle. Moreover, for the knowledge that the fractional order...
As the process of traditional dynamics modeling for rigid-flexible couple system is complex, this paper introduces the theory of characteristic modeling to simplify the modeling process. Unlike other reduced-order models, characteristic model compresses the high-order information into the characteristic parameters. Therefore, it will not lose model information. In addition, in order to improve the...
The inception to rotating stall in axial compressors with inlet distortions is theoretically investigated by studying the three state Moore-Greitzer model with periodic perturbations. The model is transformed into a normal form by using the center manifold theory. Based on the normal form, we derived analytically the periodic solutions as well as their stability boundaries. When the amplitudes of...
We explicitly construct Lyapunov functions for nonlinear systems near two types of bifurcations, namely the equilibrium bifurcations and the Hopf bifurcations. The construction relies on linear and nonlinear coordinate transformation of local center manifold and normal form. The Lyapunov functions are expected to be useful for stability and performance analysis on the effects of noises for nonlinear...
The diocotron instability of a relativistic sheet electron beam propagating through a uniform magnetic field is studied using a macroscopic cold fluid model. The general eigenvalue equation is obtained for low-frequency perturbations. In the limit of a long axial wavelength, a dispersion relation is derived for the special case of a sharp boundary density profile and used to study stability properties...
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