Multivariable fractional system approximation with initial conditions using integral state space representation

Abstract

a b s t r a c tIn this paper, we consider the approximation of general multivariable non commensurate fractional systems by integer order state space models. This work contains two main contributions. First, a new state space representation using the fractional integral operator is introduced. Second, the approximate model carries explicitly the initial conditions of the system. Two examples are given to illustrate the accuracy of the approximation.Crown

Generalized method for rational approximation of SISO/MIMO fractional-order systems using squared magnitude function

“…Rational approximation has become an important research topic in the field of FOS. Rachid et al (2010) presented a state-space approach for the rational approximation of FOS having initial conditions. Since fractional electronic circuit components are not standardized or commercially available, the approximation of FOS by an integer-order representation is required for its practical realization (Djouambi et al, 2007; Khanra, 2014; Khanra et al, 2013a).…”

Numerical analysis of the initial conditions in fractional systems

“…One of the difficulties often found by researchers consists of the initialization of fractional differential equations. In fact, while classical integer order systems require a finite set of initial conditions, fractional operators have an intrinsic memory of the phenomena that is translated into the requirement for a proper initialization and, eventually, to an infinite set of initial conditions [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. The problem becomes even more intricate when we verify that there are several possible definitions for the fractional operators, that may lead to the requirement either of integer or of fractional order initial conditions.…”