Electronic structure and surface properties of SrBi2Ta2O9 and related oxides

The electronic structure of SrBi2Ta2O9 and related oxides such as SrBi2Nb2O9, Bi2WO6 and Bi3Ti4O12 have been calculated by the tight-binding method. In each case, the band gap is about 4.1 eV and the band edge states occur on the Bi-O layers and consist of mixed O p/Bi s states at the top of the valence band and Bi p states at the bottom of the conduction band. The main difference between the compounds is that Nb 5d and Ti 4d states in the Nb and Ti compounds lie lower than the Ta 6d states in the conduction band. The surface pinning levels are found to pin Schottky barriers 0.8 eV below the conduction band edge.

H∞ sampled-data synthesis and related numerical issues

In this paper we present a new, compact derivation of state-space formulae for the so-called discretisation-based solution of the H∞ sampled-data control problem. Our approach is based on the established technique of continuous time-lifting, which is used to isometrically map the continuous-time, linear, periodically time-varying, sampled-data problem to a discretetime, linear, time-invariant problem. State-space formulae are derived for the equivalent, discrete-time problem by solving a set of two-point, boundary-value problems. The formulae accommodate a direct feed-through term from the disturbance inputs to the controlled outputs of the original plant and are simple, requiring the computation of only a single matrix exponential. It is also shown that the resultant formulae can be easily re-structured to give a numerically robust algorithm for computing the state-space matrices. © 1997 Elsevier Science Ltd. All rights reserved.