Control design for discrete‐time bilinear systems using the scalarized Schur complement

In this paper, controller design for discrete‐time bilinear systems is investigated by using sum of squares programming methods and quadratic Lyapunov functions. The class of rational polynomial controllers is considered, and necessary conditions on the degree of controller polynomials for quadratic stability are derived. Next, a scalarized version of the Schur complement is proposed. For controller design, the Lyapunov difference inequality is converted to a sum of squares problem, and an optimization problem is proposed to design a controller, which maximizes the region of quadratic stability of the bilinear system. Input constraints can also be accounted for. Copyright © 2017 John Wiley & Sons, Ltd.     

Synthesis and testing of cellulose acetate nicotinate as adsorbent for rhodamine B dye

The esterification of cellulose hydroxyl groups with natural carboxylic acids in mild conditions represents an adequate pathway in obtaining cellulose derivatives with different useful properties. In this article, authors report the synthesis of new mixed ester of cellulose and cellulose acetate nicotinate (CAN) , in a homogenous medium using DMF as solvent, cellulose acetate (CA) as starting cellulosic material, and nicotinic acid as an esterification agent in the presence of p-toluenesulfonyl chloride and pyridine. FTIR and NMR techniques were used to prove the binding of nicotinoyl group at free hydroxyl groups of CA. The obtained CAN was electrospun by electrospinning technique to obtain adsorbent ultrafine fibers, evidenced by SEM images, with high specific surface area. Monolayer Langmuir and empirical Leundrich isotherms were used to assess the adsorption capacity for rhodamine B dye of electrospun CAN in comparison with that of electrospun CA used as starting material. Langmuir isotherm led to a better assessment of experimental data suggesting that the adsorption is mainly determined by hydrogen bonds formed between carboxylic OH hydrogen bonding donor and pyridine N hydrogen bonding acceptor. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47772.     

Hierarchically structured polymer blends based on silsesquioxane hybrid nanocomposites with quaternary ammonium units for antimicrobial coatings

The paper reports the first study on hierarchical assemblies (nanofibrillar micelles confined within semi-cylindrical shells) with silsesquioxane and quaternary ammonium units obtained through polymer blending intended for antimicrobial/antifungal stone coatings. The formation of hierarchical structures on solid surfaces is due to the multiple intermolecular ionic interactions, intermolecular Van der Waals and hydrophobic interactions acting among the component molecules. Their antimicrobial/antifungal properties toward the Gram-negative bacteria, Escherichia coli, Gram-positive bacteria, Staphylococcus aureus, and Candida albicans fungus were determined in aqueous solution and were found to be strongly dependent of the topographical features of the coating.     

Cyclic invariance for discrete time-delay systems

This technical communique introduces a new concept of set invariance with respect to linear discrete time dynamics affected by delay. We are interested in the definition and characterization of sequences of cyclically invariant subsets in the state space. The algebraic conditions established in the late ’80s for linear dynamics are generalized to invariance analysis in the presence of delays for given sequences of polyhedral sets.     

Relaxing PWQ Lyapunov stability criteria for PWA systems

The note addresses the calculation of piecewise quadratic (PWQ) Lyapunov functions for PWA (piecewise affine) systems. New LMI relaxations are proposed. These relaxations have been found to be effective in cases where the traditional relaxations fail.     

A patchy approximation of explicit model predictive control

The explicit solution of multi-parametric optimisation problems (MPOP) has been used to construct an off-line solution to relatively small- and medium-sized constrained control problems. The control design principles are based on receding horizon optimisation and generally use linear prediction models for the system dynamics. In this context, it can be shown that the optimal control law is a piecewise linear (PWL) state feedback defined over polytopic cells of the state space. However, as the complexity of the related optimisation problems increases, the memory footprint and implementation of such explicit optimal solution may be burdensome for the available hardware, principally due to the high number of polytopic cells in the state-space partition. In this article we provide a solution to this problem by proposing a patchy PWL feedback control law, which intend to approximate the optimal control law. The construction is based on the linear interpolation of the exact solution at the vertices of a feasible set and the solution of an unconstrained linear quadratic regulator (LQR) problem. With a hybrid patchy control implementation, we show that closed-loop stability is preserved in the presence of additive measurement noise despite the existence of discontinuities at the switch between the overlapping regions in the state-space partition.     

Analytical and numerical computation of air-gap magnetic fields in brushless motors with surface permanent magnets

This paper extends the theory of the air-gap magnetic field in permanent-magnet (PM) brushless motors. Scalar and vector potential solutions to the field equations are brought together to unify many of the important practical methods already in use. The theory admits a more general representation of the magnetization vector than has been previously assumed, including both the radial and tangential components, and variation with radius. The work is applied in the design of PM motors where there is a requirement to minimize noise and torque ripple, and maximize efficiency, and a continuing need for improvements in the accuracy and rigor of design calculations. The air-gap flux-density distribution is at the heart of the design process, and it is desirable to study different magnetization patterns, including imperfections in the magnetization, for a wide range of magnet shapes. This paper shows the application of the analytical solutions in comparison with a new finite-element procedure, with test results on a prototype motor, and with simpler, older methods of calculation based on magnetic equivalent circuits. The comparison brings out many interesting points in relation to the accuracy and the speed and practicality of the various methods.     

Discrete‐time sector based hands‐off control for nonlinear system

This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as “discrete‐time sector.” The design method to define the boundary of a discrete‐time sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results.     

Lipid nanoparticles based on butyl-methoxydibenzoylmethane: in vitro UVA blocking effect

The aim of the present study was to obtain efficient lipid nanoparticles loaded with butyl-methoxydibenzoylmethane (BMDBM) in order to develop cosmetic formulations with enhanced UVA blocking effect. For this purpose, two adequate liquid lipids (medium chain triglycerides and squalene) have been used in combination with two solid lipids (cetyl palmitate and glyceryl stearate) in order to create appropriate nanostructured carriers with a disordered lipid network able to accommodate up to 1.5% BMDBM. The lipid nanoparticles (LNs) were characterized in terms of particle size, zeta potential, entrapment efficiency, loading capacity and in vitro UVA blocking effect. The efficiency of lipid nanoparticles in developing some cosmetic formulations has been evaluated by determining the in vitro erythemal UVA protection factor. In order to quantify the photoprotective effect, some selected cream formulations based on BMDBM-LNs and a conventional emulsion were exposed to photochemical UV irradiation at a low energy to simulate the solar energy during the midday. The results obtained demonstrated the high ability of cream formulations based on BMDBM-LNs to absorb more than 96% of UVA radiation. Moreover, the developed cosmetic formulations manifest an enhanced UVA blocking effect, the erythemal UVA protection factor being four times higher than those specific to conventional emulsions.