Robust state derivative feedback LMI-based designs for discretized systems.

This work addresses novel Linear Matrix Inequality (LMI)-based conditions for thedesign of discrete-time state derivative feedback controllers. The main contribution of this work consists of an augmented discretized model formulated in terms of the state derivative, such that uncertain sampling periods and parametric uncertainties in polytopic form can be propagated from the original continuous-time state space representation. The resulting discrete-time model is composed of homogeneous polynomial matrices with parameters lying in the Cartesian product of simplexes, plus an additive norm-bounded term representing the residual discretization error. Moreover, the referred condition allows for the closed-loop poles allocation of the augmented system in a D-stable region. Finally, numerical simulations illustrate the effectiveness of the proposed method.

Numerical Solution of the Navier–Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers

Multigrid methods (MGMs) are used for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier–Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAEs) with a strongly non-Hermitian matrix appear. Hermitian/skew-Hermitian splitting (HSS) and skew-Hermitian triangular splitting (STS) methods are considered as smoothers in the MGM for solving the SLAE. Numerical results for an algebraic multigrid (AMG) method with HSS-based smoothers are presented.

Linearization and discretization risks in knowledge management

The purpose of this paper is to analyze the limitations induced in Knowledge Management by the processes of linearization and discretization, which happen frequently in decision-making. Linearization is a result of applying linear thinking models in decision-making, regardless of the complexity of knowledge management phenomena. Knowledge and all the other intangible resources are nonlinear entities and they should be evaluated with nonlinear metrics. However, in many situations managers use simple solutions based on linear thinking models and get large errors in their decision-making, with significant negative consequences in management. Also, linear thinking model is dominant in legislation, which may lead to significant errors in managerial decision-making. Discretization is a process in which an entity with a continuous representation, like a knowledge field, is transformed into a piecewise entity to be handled more easily. Also, social media uses discretized systems for different evaluations which should be interpreted accordingly. For instance, counting the number of “like” on Facebook for a certain message or image may lead to the conclusion that friendship is proportional with the number of “friends”, which might not be in concordance with reality. Knowledge management is a complex activity dealing with knowledge, which means nonlinear entities. Using linear thinking models and discretization methods in evaluations and decision-making may lead to significant errors and negative consequences.

New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions

This paper tackles important problems in stable discretization of commensurate fractional-order continuous-time LTI SISO systems based on the Grünwald-Letnikov (GL) difference. New, analytical stability/instability conditions are given for the GL-discretized systems governed by fractional-order transfer functions. A stability preservation analysis is also performed for a class of finite GL approximators.

Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems

We propose two variants of tailored finite point (TFP) methods for discretizing two dimensional singular perturbed eigenvalue (SPE) problems. A continuation method and an iterative method are exploited for solving discretized systems of equations to obtain the eigen-pairs of the SPE. We study the analytical solutions of two special cases of the SPE, and provide an asymptotic analysis for the solutions. The theoretical results are verified in the numerical experiments. The numerical results demonstrate that the proposed schemes effectively resolve the delta function like of the eigenfunctions on relatively coarse grid.