We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as a subspace fitting problem and analyze the difference between the solution su...

The main difficulty in stability analysis of reset control systems comes from their state-dependent reset mechanism. It becomes more challenging when output matrix suffers from uncertainties which make the reset time instants uncertain. In this paper, existing quadratic stability results for uncertainty-free reset systems are extended to the case with uncertainty in the output matrix. By constr...

The transfer-matrix methodology is frequently used to deal with elastic scattering problems that require a solution of the Schrödinger or homogeneous Maxwell equations in the continuous part of their spectra. In its basic formulation, this technique however reveals limited by numerical instabilities, which can be drastically reduced by application of the layer addition algorithm. By providing e...

We provide new theoretical results on the generalization properties of learning algorithms for multiclass classification problems. The originality of our work is that we propose to use the confusion matrix of a classifier as a measure of its quality; our contribution is in the line of work which attempts to set up and study the statistical properties of new evaluation measures such as, e.g. ROC...

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nickel hydroxide nanostructures were synthesized by a hydrothermal reaction. the effect of different precursors and surfactants on the morphology of nickel hydroxide nanostructures was investigated. nanostructures were characterized by x-ray diffraction, energy dispersive x-ray spectroscopy, scanning electron microscopy and fourier transform infrared  spectroscopy. the influence of ni(oh)2 nano...

In this paper, the problem of delay dependent robust asymptotically stable for uncertain linear time-variant system with multiple delays is investigated. A new delay-dependent stability sufficient condition is given by using the Lyapunov method, linear matrix inequality (LMI), parameterized first-order model transformation technique and transformation of the interval uncertainty in to the norm ...

Nickel hydroxide nanostructures were synthesized by a hydrothermal reaction. The effect of different precursors and surfactants on the morphology of nickel hydroxide nanostructures was investigated. Nanostructures were characterized by X-ray diffraction, energy dispersive X-ray spectroscopy, scanning electron microscopy and Fourier transform infrared  spectroscopy. The influence of Ni(OH)2 nano...

New Schur stability checking method of the polynomial matrices whose coefficient matrix are interval matrices is presented in this paper. In the suggested method, the interval Markov matrices of the interval polynomial matrix are used to assess its stability. The validity of the suggested methods is illustrated through numerical examples. The main contribution of the suggested method is that it...

The notion of “strong stability” has been introduced in a recent paper [KHP2]. This notion is relevant for state-space models described by physical variables and prohibits overshooting trajectories in the state-space transient response for arbitrary initial conditions. Thus, “strong stability” is a stronger notion compared to alternative definitions (e.g. stability in the sense of Lyapunov or a...