Reach set computation is a basic component of many veri cation and control synthesis procedures. E ective computation schemes are available for discrete systems described by nite state machines and continuous-variable systems described by linear di erential inequalities. This paper suggests an approach based on the Pontryagin maximum principle of optimal control theory. The approach is elaborat...

A formal correspondence is established between the curvature theory of generalized implicit hypersurfaces, the classical theory of electromagnetism as expressed in terms of exterior di®erential systems, and thermodynamics. Starting with a generalized implicit surface whose normal ̄eld is represented by an exterior di®erential 1-form, it is possible to deduce the curvature invariants of the impl...

This report presents experimental results for new NAG Fortran Library software for the solution of large sparse symmetric linear systems of algebraic equations Preconditioned conjugate gradient methods introduced at Mark are compared against iterative and direct methods previously available in the library Test problems include discrete approximations to d elliptic partial di erential equations ...

In this paper, the problem of the stability analysis for neutral delay-di€ erential systems with nonlinear perturbations is investigated. Using the L yapunov method, we present new su cient conditions for the stability, in terms of the linear matrix inequality (LMI), which can be easily solved by various convex optimization algorithms. Numerical examples are given to illustrate the application...

A detailed description is given of the parallel algorithms used in AUTO94P, an experimental parallel version of the software AUTO for the numerical bifurcation analysis of systems of ordinary di erential equations. Timing results and user instructions for the Intel Delta are included. The sequential version of the software, AUTO94, is fully described in [8]. For a related tutorial paper see [5,...

A detailed description is given of the parallel algorithms used in AUTO94P, an experimental parallel version of the software AUTO for the numerical bifurcation analysis of systems of ordinary di erential equations. Timing results and user instructions for the Intel Delta are included. The sequential version of the software, AUTO94, is fully described in [8]. For a related tutorial paper see [5,...

The task of modeling, i.e. of creating a set of equations that can be used to predict the behavior of a physical object, is a key step in engineering analysis. This paper describes a computer system, MSG, for generating mathematical models to analyze physical systems involving heat transfer behavior. MSG is motivated by the need for modeling in an automated design process. The models are sets o...

A transformation is introduced to e!ectively remove level e!ects, i.e. the state dependency of the di!usion function, in a restricted class of multivariate stochastic di!erential equations such that the general continuous}discrete-time nonlinear "ltering problem may be solved using new or existing implementations of the extended kalman "lter (EKF). An implementation of a quasi-maximum likelihoo...

In this paper we discuss stochastic di erential delay equations with Markovian switching. Such an equation can be regarded 9 as the result of several stochastic di erential delay equations switching from one to another according to the movement of a Markov chain. The aim of this paper is to investigate the stability in distribution of the equations. 11 c © 2003 Published by Elsevier Science B.V.