A method for modelling and simulation of fractional systems
Signal Processing - Special issue: Fractional signal processing and applications
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Fractional order control: a tutorial
ACC'09 Proceedings of the 2009 conference on American Control Conference
Brief State-space representation for fractional order controllers
Automatica (Journal of IFAC)
Fractional models for modeling complex linear systems under poor frequency resolution measurements
Digital Signal Processing
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A large number of real dynamic systems are better characterized using a non-integer order dynamic model based on fractional order differential equations. Nevertheless, their analytical solutions are rather complicated. In this paper we present two alternative methods of simulation of the fractional order dynamical system in state space. We particularly present a comparison between two approximation methods. The first one is based on the differentiation operator approximation and thus uses the usual form of the state space representation D^(^@a^)(x)=Ax+Bu. The second method is based on the approximation of the integration operator and uses, in this case, the new representation w=AI^(^@a^)(w)+Bu. The comparison between these two methods is made on the basis of initial and steady state approximation state and output errors which are characterized in this present paper. Numerical examples are also given to support this comparison.