2,374 research outputs found
Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy
We update gamma-ray burst (GRB) luminosity relations among certain spectral
and light-curve features with 139 GRBs. The distance modulus of 82 GRBs at
can be calibrated with the sample at by using the cubic
spline interpolation method from the Union2.1 Type Ia supernovae (SNe Ia) set.
We investigate the joint constraints on the Cardassian expansion model and dark
energy with 580 Union2.1 SNe Ia sample () and 82 calibrated GRBs data
(). In CDM, we find that adding 82 high-\emph{z} GRBs to
580 SNe Ia significantly improves the constrain on
plane. In the Cardassian expansion model, the
best fit is and
, which is consistent with the CDM cosmology in the
confidence region. We also discuss two dark energy models in which
the equation of state is parametrized as and
, respectively. Based on our analysis, we see that our
Universe at higher redshift up to is consistent with the concordance
model within confidence level.Comment: 17 pages, 6 figures, 2 tables; accepted for publication in Advances
in Astronomy, special issue on Gamma-Ray Burst in Swift and Fermi Era. arXiv
admin note: text overlap with arXiv:0802.4262, arXiv:0706.0938 by other
author
Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching
A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case
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