Model reduction for linear differential inclusions: robustness and time-variance

This paper deals with the problem of model reduction by moment matching for linear differential inclusions. The problem is formally formulated and the notions of moment- set, perturbed moment trajectory, approximate reduced order model and robust reduced order model are introduced. Two sets of results are presented. The first part of the paper deals with robustness of the reduced order models with respect to input perturbations. Exploiting this result an enhanced model reduction scheme for linear differential equations is presented. In the second part of the paper we focus on the problem of model reduction by moment matching for time-varying systems driven by time-varying signal generators. Finally, these two sets of results are used to solve the problem of model reduction for linear differential inclusions. The results are illustrated by means of numerical examples

Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals, and System

An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Pyrite-induced hydroxyl radical formation and its effect on nucleic acids

BACKGROUND: Pyrite, the most abundant metal sulphide on Earth, is known to spontaneously form hydrogen peroxide when exposed to water. In this study the hypothesis that pyrite-induced hydrogen peroxide is transformed to hydroxyl radicals is tested. RESULTS: Using a combination of electron spin resonance (ESR) spin-trapping techniques and scavenging reactions involving nucleic acids, the formation of hydroxyl radicals in pyrite/aqueous suspensions is demonstrated. The addition of EDTA to pyrite slurries inhibits the hydrogen peroxide-to-hydroxyl radical conversion, but does not inhibit the formation of hydrogen peroxide. Given the stability of EDTA chelation with both ferrous and ferric iron, this suggests that the addition of the EDTA prevents the transformation by chelation of dissolved iron species. CONCLUSION: While the exact mechanism or mechanisms of the hydrogen peroxide-to-hydroxyl radical conversion cannot be resolved on the basis of the experiments reported in this study, it is clear that the pyrite surface promotes the reaction. The formation of hydroxyl radicals is significant because they react nearly instantaneously with most organic molecules. This suggests that the presence of pyrite in natural, engineered, or physiological aqueous systems may induce the transformation of a wide range of organic molecules. This finding has implications for the role pyrite may play in aquatic environments and raises the question whether inhalation of pyrite dust contributes to the development of lung diseases

Recent progress and perspectives of space electric propulsion systems based on smart nanomaterials

Miniaturized spacecraft built from advanced nanomaterials are poised for unmanned space exploration. In this review, the authors examine the integration of nanotechnology in electric propulsion systems and propose the concept of self-healing and adaptive thrusters