This paper has been withdrawn. This paper focuses on the admissibility condition for fractional-order singular system with order $alpha in (0,1)$. The definitions of regularity, impulse-free and admissibility are given first, then a sufficient and necessary condition of admissibility for fractional-order singular system is established. A numerical example is included to illustrate the proposed condition.
The issues of robust stability for two types of uncertain fractional-order systems of order $alpha in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust stability is given; for the norm-bounded uncertainty case, a sufficient and necessary condition of robust stability is presented. Both of these conditions can be checked by solving sets of linear matrix inequalities. Two numerical examples are presented to confirm the proposed conditions.
To describe and analyze the dynamics of Self-Organized Criticality (SOC) systems, a four-state continuous-time Markov model is proposed in this paper. Different to computer simulation or numeric experimental approaches commonly employed for explaining the power law in SOC, in this paper, based on this Markov model, using E.T.Jayness Maximum Entropy method, we have derived a mathematical proof on the power law distribution for the size of these events. Both this Makov model and the mathematical proof on power law present a new angle on the universality of power law distributions, they also show that the scale free property exists not necessary only in SOC system, but in a class of dynamical systems which can be modelled by the proposed Markov model.
