Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition

In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage to an earlier algorithm is demonstrated. Furthermore an example is given which shows how to analyze a given perturbed interconnected system.Comment: 30 pages, 7 figures, 4 table

Tunable sub-luminal propagation of narrowband x-ray pulses

Group velocity control is demonstrated for x-ray photons of 14.4 keV energy via a direct measurement of the temporal delay imposed on spectrally narrow x-ray pulses. Sub-luminal light propagation is achieved by inducing a steep positive linear dispersion in the optical response of ${}^{57}$Fe M\"ossbauer nuclei embedded in a thin film planar x-ray cavity. The direct detection of the temporal pulse delay is enabled by generating frequency-tunable spectrally narrow x-ray pulses from broadband pulsed synchrotron radiation. Our theoretical model is in good agreement with the experimental data.Comment: 8 pages, 4 figure

The Beagle 2 microscope

The Beagle 2 microscope provides optical images of the Martian surface at a resolution 5x higher than any other experiment currently planned. By using a novel illumination system it images in three colors and can also detect fluorescent materials

Nuclear Resonance Vibrational Spectroscopy of Iron Sulfur Proteins

Nuclear inelastic scattering in conjunction with density functional theory (DFT) calculations has been applied for the identification of vibrational modes of the high-spin ferric and the high-spin ferrous iron-sulfur center of a rubredoxin-type protein from the thermophylic bacterium Pyrococcus abysii

Observation of insulator-metal transition in EuNiO3_{3} under high pressure

The charge transfer antiferromagnetic (T$_{N}$ =220 K) insulator EuNiO$_{3}$ undergoes, at ambient pressure, a temperature-induced metal insulator MI transition at T$_{MI}$=463 K. We have investigated the effect of pressure (up to p~20 GPa) on the electronic, magnetic and structural properties of EuNiO$_{3}$ using electrical resistance measurements, {151}^Eu nuclear resonance scattering of synchrotron radiation and x-ray diffraction, respectively. With increasing pressure we find at p$_{c}$ =5.8 GPa a transition from the insulating state to a metallic state, while the orthorhombic structure remains unchanged up to 20 GPa. The results are explained in terms of a gradual increase of the electronic bandwidth with increasing pressure, which results in a closing of the charge transfer gap. It is further shown that the pressure-induced metallic state exhibits magnetic order with a lowervalue of T$_{N}$ (T$_{N}$ ~120 K at 9.4 GPa) which disappears between 9.4 and 14.4 GPa.Comment: 10 pages, 3 figure

Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

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