Robust L2–L∞ control of uncertain differential linear repetitive processes

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdFor two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretical and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L2–L∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L2–L∞ static state feedback controller and an L2–L∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L2–L∞ performance. Sufficient conditions for the existence of such L2–L∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L2–L∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Filtering for uncertain 2-D discrete systems with state delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.This paper is concerned with the problem of robust H∞ filtering for two-dimensional (2-D) discrete systems with time-delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini–Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.This work was partially supported by the National Natural Science Foundation of China (60504008), Program for New Century Excellent Talents in University of China and the Postdoctoral Science Foundation of China (20060390231)

Intense terahertz laser fields on a two-dimensional electron gas with Rashba spin-orbit coupling

The spin-dependent density of states and the density of spin polarization of an InAs-based two-dimensional electron gas with the Rashba spin-orbit coupling under an intense terahertz laser field are investigated by utilizing the Floquet states to solve the time-dependent Schr\"odinger equation. It is found that both densities are strongly affected by the terahertz laser field. Especially a terahertz magnetic moment perpendicular to the external terahertz laser field in the electron gas is induced. This effect can be used to convert terahertz electric signals into terahertz magnetic ones efficiently.Comment: 3 pages, 3 figures, a typo in Fig. 3(b) is correcte

Insulating state and the importance of the spin-orbit coupling in Ca3_3CoRhO6_6

We have carried out a comparative theoretical study of the electronic structure of the novel one-dimensional Ca$_3$CoRhO$_6$ and Ca$_3$FeRhO$_6$ systems. The insulating antiferromagnetic state for the Ca$_3$FeRhO$_6$ can be well explained by band structure calculations with the closed shell high-spin $d^5$ (Fe$^{3+}$) and low-spin $t_{2g}^{6}$ (Rh$^{3+}$) configurations. We found for the Ca$_3$CoRhO$_6$ that the Co has a strong tendency to be $d^7$ (Co$^{2+}$) rather than $d^6$ (Co$^{3+}$), and that there is an orbital degeneracy in the local Co electronic structure. We argue that it is the spin-orbit coupling which will lift this degeneracy thereby enabling local spin density approximation + Hubbard U (LSDA+U) band structure calculations to generate the band gap. We predict that the orbital contribution to the magnetic moment in Ca$_3$CoRhO$_6$ is substantial, i.e. significantly larger than 1 $\mu_B$ per formula unit. Moreover, we propose a model for the contrasting intra-chain magnetism in both materials.Comment: 7 pages, 4 figures, and 1 tabl