In this paper, we combine a descriptor approach to stability and control of linear systems with time-varying delays, which is based on the Lyapunov Krasovskii techniques, with a recent result on sliding mode control of such systems. The systems under consideration have norm-bounded uncertainties and uncertain bounded delays. The solution is given in terms of linear matrix inequalities (LMIs) an...

This paper deals with the problem of observer-based stabilization for linear systems with parameter inequality. A new design methodology is proposed thanks to a judicious use of the famous Young relation. This latter leads to a less restrictive synthesis condition, expressed in term of Linear Matrix Inequality (LMI), than those available in the literature. Numerical comparisons are provided in ...

This paper presents a dual of a general linear fractional functions programming problem. Dual is shown to be a linear programming problem. Along with other duality theorems, complementary slackness theorem is also proved. A simple numerical example illustrates the result.

However, there are strong connections between these approaches when we deal with a binary target attribute. In this particular case, we can even recreate the outputs of the linear discriminant analysis with a linear regression program (Bishop, 2007, pages 189 190; Duda et al., 2001, pages 242 – 243; Huberty et Olejnik, 2006, pages 353 – 355; Nakache et Confais, 2003, pages 14 – 16; Saporta, 200...

in this study, the mechanical behavior of vanyar dam was evaluated at the end of construction. a two-dimensional numerical analysis was conducted based on a finite element method on the largest cross-section of the dam. the data recorded by the instruments located in the largest cross-section were compared with the results of the numerical analysis at the place of instruments. the settlement, p...

In this paper, we apply the  homotopy analysis method (HAM) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the ...

We investigate numerical techniques to locate the event points of the differential system x′ = f(x), characterized by a vector field f which is a discontinuous function along an event surface Σ = {x ∈ R| h(x) = 0} splitting the state space into two different regions R1 and R2, particularly f(x) = fi(x) when x ∈ Ri, for i = 1, 2 and f1(x) 6= f2(x) when x ∈ Σ. We propose event location techniques...

We present a formula for the corner points of the multi-dimensional Hausdorff polytopes and show how this result can be used to improve linear programming models for computing, e. g., moments of exit time distributions of diffusion processes. Specifically, we compute the mean exit time of two-dimensional Brownian motion from the unit square, as well as higher moments of the exit time of time-sp...

In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix A is known. Further, the hierarchical algorithm can be used to recover the d largest singular values and left singular vectors with bounded error. We also show that the proposed...