Finite-region stability of 2-D singular Roesser systems with directional delays

In this paper, the problem of finite-region stability is studied for a class of two-dimensional (2-D) singular systems described by using the Roesser model with directional delays. Based on the regularity, we first decompose the underlying singular 2-D systems into fast and slow subsystems corresponding to dynamic and algebraic parts. Then, with the Lyapunov-like 2-D functional method, we construct a weighted 2-D functional candidate and utilize zero-type free matrix equations to derive delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). More specifically, the derived conditions ensure that all state trajectories of the system do not exceed a prescribed threshold over a pre-specified finite region of time for any initial state sequences when energy-norms of dynamic parts do not exceed given bounds

Curie Temperature of Diluted Magnetic Semiconductors: the Influence of the Antiferromagnetic Exchange Interaction

The coherent potential approximation and mean field approximation are used to calculate the free energy of the coupled carrier – localized spin system in III-V diluted magnetic semiconductors. Thus the magnetic transition temperature Tc can be determined and its dependence on important model parameters. We show that the strong antiferromagnetic superexchange interaction between nearest neighbour sites considerably reduces the Curie temperature