In this chapter, we propose to use a parametric multiplier approach to deriving parametric Lyapunov functions for robust stability analysis of linear systems involving uncertain parameters. This new approach generalizes the traditional multiplier approach used in the absolute stability literature where the multiplier is independent of the uncertain parameters. Our main result provides a general...

Adler and Monteiro (1992) developed a parametric analysis approach that is naturally related to the geometry of the linear pro~am. This approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity. In this paper, we develop an altemative geometric approach for parametric analysis which does not require the strong complementarity condition. This pa...

Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of Kernel Estimation is developed for univariate and multivariate settings. The second section discusses some of the applications of Kernel Estimation to high-...

This thesis contains five chapters. The notations, terminologies, definitions and numbering of equations, theorems and algorithms are independent in each chapter. Chapter 1 provides a fundamental introduction and contextual discussions to provide a unified theme for the subsequent chapters into a complete work. Chapters 2, 3 and 4 are arranged for ease of reading and understanding separately. F...

Measuring the volume of heart ventricles is an important issue in heart disease diagnosis. Therefore radiologists investigate computer tomographic images, searching for representative projections of the left ventricle. In the selected image showing the left ventricle with maximum circumference, a parametric model is established by measuring width and height of the left ventricle shape. These pa...

Optical parametric chirped pulse amplification (OPCPA) is one of the most powerful techniques for generating high-energy femtosecond laser pulses. Many efforts were devoted to get spectral-band amplification able to support sub-10-fs pulses. In the optical parametric amplification (OPA), broad gain bandwidths can be obtained if the wave-vectors mismatch, ∆k, slowly increases when the signal fre...

Several linear methods of residual generation for fault detection and diagnosis are reviewed. The parity relation approach is introduced in some detail, for both additive and parametric faults. The Chow–Willsky scheme, various diagnostic observers and principal component analysis are compared to the additive version. The ‘local approach’ and the least-squares estimation of parameter changes are...

The problem of evaluating the solvency of insurance companies is tackled through the use of parametric and non-parametric statistical models, constructed using respectively multivariate methodologies and decision-tree techniques. First we intend to present the theoretical framework of both methodologies describing them within a Bayesian context, then two models are tested on a sample of Italian...