A new result on the delay‐dependent stability of discrete systems with time‐varying delays

This paper proposes an improvement to the delay‐dependent stability of discrete systems with time‐varying delays. The approach is based on the observation that the positive definiteness of a chosen Lyapunov–Krasovskii functional does not necessarily require all the involved symmetric matrices to be positive definite, which has been overlooked in the literature. The derived delay‐dependent stability conditions are in terms of linear matrix inequalities. It is theoretically proved that our results are less conservative than the corresponding ones obtained by requiring the positive definiteness of all the symmetric matrices in a chosen Lyapunov–Krasovskii functional. The importance of the present approach is that a great number of delay‐dependent analysis and synthesis results obtained by the aforementioned requirement in the literature can be improved by the present approach without introducing any new decision variables. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of platinum and silver deposits in the photocatalytic oxidation of resorcinol

The effects of platinum (Pt) and silver (Ag) metallisation in the photocatalytic oxidation of resorcinol at pH 3 ± 0.5 have been investigated. The photocatalytic degradation of resorcinol was significantly improved by Pt/TiO₂, while the presence of Ag/TiO₂ enhanced the initial photocatalytic degradation rate of resorcinol slightly. Likewise, the photocatalytic mineralisation of resorcinol continued to be enhanced by Pt/TiO₂, but it was retarded when Ag/TiO₂ was used.

The function of Pt and Ag deposits on the surface of TiO₂ has been found to be markedly influenced by the interaction of resorcinol and its degradation products with the metal deposits. The presence of Pt or Ag on the surface of TiO₂ altered the distribution of degradation products of resorcinol as well as the production of photoactive species for the photocatalytic oxidation of resorcinol. The X-ray photoelectron spectroscopy (XPS), zeta potential and transmission electron microscopy (TEM) analyses have indicated that the contrasting effect of Pt and Ag deposits were governed by the oxidation states and the catalytic property of metal deposits. In addition to that, it has been found that the roles of metal deposits are specific and should not be generalised.     

Effect of nano‐silica filler on the rheological and morphological properties of polypropylene/liquid‐crystalline polymer blends

A fumed hydrophilic nano‐silica‐filled polypropylene (PP) composite was blended with a liquid‐crystalline polymer (LCP; Rodrun LC5000). The preblended polymer blend was extruded through a capillary die; this was followed by a series of rheological and morphological characterizations. The viscosity of the PP matrix increased with the addition of the hydrophilic nano‐silica. At shear rates between 50 and 200 s^?1, the composite displays marked shear‐thinning characteristics. However, the incorporation of LC5000 in the PP composite eliminated the shear‐thinning characteristic, which suggests that LC5000 destroyed the agglomerated nano‐silica network in the PP matrix. Although the viscosity ratio of LCP/PP was reduced after the addition of nano‐silica fillers, the LCP phases existed as droplets and ellipsoids. The nano‐silicas were concentrated in the LC5000 phase, which hindered the formation of LCP fibers when processed at high shear deformation. We carried out surface modification of the hydrophilic nano‐silica to investigate the effect of modified nano‐silica (M‐silica) on the morphology of the PP/LC5000 blend system. Ethanol was successfully grafted onto the nano‐silica surface with a controlled grafting ratio. The viscosity was reduced for PP filled with ethanol‐M‐silica when compared to the system filled with untreated hydrophilic nano‐silica. The LC5000 in the (PP/M‐silica)/LC5000 blend existed mainly in the form of fibrils. At high shear rates (e.g., 3000 s^?1), the LC5000 fibril network was formed at the skin region of the extrudates. The exclusion of nano‐silica in the LC5000 phase and the increased viscosity of the matrix were responsible for the morphological changes of the LCP phase. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1484–1492, 2003     

Synthesis of novel tri- and tetrasubstituted C<Subscript>18</Subscript> furan fatty esters

A methylene-interrupted C₁₈ keto-acetylenic fatty ester (methyl 12-oxo-9-octadecynoate) was obtained from methyl ricinoleate by bromination-dehydrobromination followed by oxidation. Reaction of methyl 12-oxo-9-octadecynoate with bis(benzonitrile) palladium(II) chloride, allyl bromide, or methyl-allyl bromide furnished methyl 8-[5-hexyl-3-allyl-furan-2-yl]-octanoate (1, 56%) or methyl 8-[5-hexyl-3-(2-methyl-allyl)-furan-2-yl]-octanoate (2, 55%). Reaction of methyl 12-oxo-11-chloro-or 11-fluoro-9-octadeyynoate (prepared from methyl santalbate-methyl 11-E-9-octadecynoate, found in sandalwood, Santalum album, seed oil) with bis(benzonitrile) palladium(II) chloride gave methyl 8-(4-fluoro-5-hexyl-furan-2-yl)-octanoate (3, 50%) or methyl 8-(4-fluoro-5-hexyl-furan-2-yl)-octanoate (4, 50%), respectively. And when methyl 12-oxo-11-chloro- or 11-fluoro-9-octadecynoate was treated with a mixture of bis(benzonitrile) palladium(II) chloride, allyl bromide, or methyl-allyl bromide, the reaction yielded tetrasubstituted C₁₈ furan derivatives, viz, methyl 8-(3-allyl-4-chloro-5-hexyl-furan-2-yl)-octanoate (5, 54%), methyl 8-[4-chloro-5-hexyl-3-(2-methyl-allyl)-furan-2-yl)-octanoate (6, 54%), methyl 8-(3-allyl-4-fluoro-5-hexyl-furan-2-yl]-octanoate (7, 10%), and methyl 8-[4-fluoro-5-hexyl-3-(2-methyl-allyl)-furan-2-yl]-octanoate (8, 10%). The presence of a fluorine atom in the furan derivatives 4, 7, and 8 was readily characterized by the appearance of doublets for carbon nuclei, which were coupled to the fluorine atom in the ¹³C NMR spectra. All furan fatty derivatives from this work were characterized by NMR spectroscopic and mass spectrometric analyses. The yields of compounds 7 and 8 were very low (10%) despite attempts to improve the procedure by increasing the amounts of the reactants and catalyst.     

Positivity and stability of mixed fractional‐order systems with unbounded delays: Necessary and sufficient conditions

This article provides a comprehensive study on quantitative properties of linear mixed fractional‐order systems with multiple time‐varying delays. The delays can be bounded or unbounded. We first obtain a result on existence and uniqueness of solutions to these systems. Then, we prove a necessary and sufficient condition for their positivity. Finally, we provide a necessary and sufficient criterion to characterize asymptotic stability of positive linear mixed fractional‐order systems with multiple time‐varying delays.     

Micro cam system driven by electrostatic comb-drive actuators based on SOI-MEMS technology

Microsystem Technologies - This paper reports a design and fabrication process of a micro cam system (MCS) with a flat-faced translating follower. The cam rim with cover diameter of 2.4&nbsp;mm...     

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

This paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

H∞ Control with Transients for Singular Systems

In this paper, the problem of a generalized type of H_∞ control is investigated for continuous‐time singular systems, which treats a mixed attenuation of exogenous inputs and initial conditions. First, a performance measure that is essentially the worst‐case norm of the regulated outputs over all exogenous inputs and initial conditions is introduced. A necessary and sufficient condition is obtained to ensure the singular system to be admissible and the performance measure to be less than a prescribed scalar. Based on the criterion a sufficient condition for the existence of a state‐feedback controller is established in terms of linear matrix inequalities. Moreover, the relationship between the performance measure and the standard H_∞ norm of the system is provided. Two numerical examples are given to demonstrate the properties of the obtained results.     

A scalable, self-analyzing digital locking system for use on quantum optics experiments

Digital control of optics experiments has many advantages over analog control systems, specifically in terms of the scalability, cost, flexibility, and the integration of system information into one location. We present a digital control system, freely available for download online, specifically designed for quantum optics experiments that allows for automatic and sequential re-locking of optical components. We show how the inbuilt locking analysis tools, including a white-noise network analyzer, can be used to help optimize individual locks, and verify the long term stability of the digital system. Finally, we present an example of the benefits of digital locking for quantum optics by applying the code to a specific experiment used to characterize optical Schr?dinger cat states.     

A Stochastic Vehicle Routing Problem with Travel Time Uncertainty: Trade-Off Between Cost and Customer Service

On-time shipment delivery is critical for just-in-time production and quick response logistics. Due to uncertainties in travel and service times, on-time arrival probability of vehicles at customer locations can not be ensured. Therefore, on-time shipment delivery is a challenging job for carriers in congested road networks. In this paper, such on-time shipment delivery problems are formulated as a stochastic vehicle routing problem with soft time windows under travel and service time uncertainties. A new stochastic programming model is proposed to minimize carrier’s total cost, while guaranteeing a minimum on-time arrival probability at each customer location. The aim of this model is to find a good trade-off between carrier’s total cost and customer service level. To solve the proposed model, an iterated tabu search heuristic algorithm was developed, incorporating a route reduction mechanism. A discrete approximation method is proposed for generating arrival time distributions of vehicles in the presence of time windows. Several numerical examples were conducted to demonstrate the applicability of the proposed model and solution algorithm.