In this paper, a new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of uncertain systems easily by solving some LMIs. A rigorous proof is given to s...

In this paper we provide algorithms based on Linear Matrix Inequalities for the design of fullauthority and external linear anti-windup compensators of reduced order guaranteeing finite global L2 gain. Previous results showed that the reduced order anti-windup design problem is non-convex. We propose here a convex approximation of the non-convex constraints leading to constructive design algori...

Observer-based stabilisation of linear systems with parameter uncertainties by using enhanced LMI conditions Houria Kheloufi, Fazia Bedouhene, Ali Zemouche & Angelo Alessandri a Department of Mathematics, Laboratoire de Mathématiques Pures et Appliquées, University Mouloud Mammeri, Tizi-Ouzou, BP No. 17 RP 15000, Algeria b Department of Automatic, University of Lorraine, 186, rue de Lorraine, C...

A method is proposed for studying robust stability of uncertain linear systems subject to actuator saturation. It hinges upon successive LMI relaxations and therefore can readily be implemented using widely available numerical tools. The technique is illustrated on two examples and is shown to signiicantly improve previously published results.

We give linear-inequalities-based sufficient conditions for the unsolvability and solvability of the NP-hard absolute value equation (AVE): Ax − |x| = b, where A is an n × n square matrix. The satisfaction of the linear inequalities is easily verified using a linear program.

The paper considers social welfare functions and ethical inequality measures for linear inequality concepts when households may differ in needs. The welfare functions are nested, i.e. separable in the level of welfare attained by the homogeneous subpopulations, and possess a homogeneity property depending on the inequality concept imposed. Several principles of transfers between different house...

In this work, we establish Hölder’s inequality, Minkowski’s inequality and Jensen’s inequality on time scales via the nabla integral and diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals. c © 2008 Published by Elsevier Ltd

OBJECTIVE To examine the relation between county-level income inequality and rates of child maltreatment. METHODS Data on substantiated reports of child abuse and neglect from 2005 to 2009 were obtained from the National Child Abuse and Neglect Data System. County-level data on income inequality and children in poverty were obtained from the American Community Survey. Data for additional cont...

An important class of optimization problems in control and signal processing involves the constraint that a Popov function is nonnegative on the unit circle or the imaginary axis. Such a constraint is convex in the coefficients of the Popov function. It can be converted to a finitedimensional linear matrix inequality via the Kalman-Yakubovich-Popov lemma. However, the linear matrix inequality r...

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder'...