In this paper we transfer classical results concerning Lyapunov stability of stationary solutions x to the classes of DAEs being most interesting for circuit simulation, thereby keeping smoothness as low as possible. We formulate all criteria in terms of the original equation. Those simple matrix criteria for checking regularity, Lyapunov stability etc. are easily realized numerically.

We synthesize robust nonlinear static output feedback controllers for systems of quasi-linear parabolic partial di!erential equations with time-dependent spatial domains and uncertain variables. The controllers are successfully applied to a typical di!usion}reaction process with moving boundary and uncertainty. ( 2000 Elsevier Science Ltd. All rights reserved.

The semi-implicit Euler discretization method is studied for abstract evolution equations in a Hilbert space H, like _ u = f(t; u; u) ; t 2 (0; T ] ; u(0) = u0, where f(t; ; v) is one-sided Lipschitz and R(I hf(t; ; v)) = H for h > 0 su ciently small, and f(t; u; ) is Lipschitz-continuous. Extension to Banach spaces is then pointed out. Ordinary and partial , di erential and integro-di erential...

In technological computer aided design (TCAD), advanced pre-processors generate the mathematical models automatically. Network approaches enable the handling of complex applications with several thousand or more equations. Since most network descriptions rely on redundant coordinates, the corresponding models lead to descriptor forms or diierential-algebraic equations. Such coupled systems of o...

The purpose of this paper is to extend to a ne in the control stochastic di erential systems the well{known result of Jurdjevic{Quinn [2]. This result incorporates a previous result in the stochastic context proved in [1].

Mycobacterium smegmatis contains three chaperonin (cpn60) genes homologous to the Escherichia coli groEL gene. One of these (cpn60.1) is required for biofilm formation, but is nonessential, whereas a second (cpn60.2) is essential. Mycobacterium smegmatis is unique among Mycobacteria in having a third chaperonin gene, cpn60.3. The cpn60.1 gene has a gene upstream (cpn10) that is homologous to th...

| In this short note we present an observability criterion for systems whose state is governed by a matrix Riccati di erential equation and whose output is given by an a ne transformation.

In this paper we present some results about analytic machines regarding the power of computations over Q or R solutions of di erential equations and the stability problem of dynamical systems We rst explain the machine model which is a kind of Blum Shub Smale machine enhanced by in nite convergent computations Next we com pare the computational power of such machines over the elds Q and R showi...

The problem of learning qualitative models of physical systems from observations of its behaviour has been addressed by several researchers in recent years. Most current techniques limit themselves to learning a single qualitative di erential equation to model the entire system. However, many systems have several qualitative differential equations underlying them. In this paper, we present an a...

This paper deals with development and analysis of a fully discrete nite element method for a nonlinear di erential system for describing an air water system in groundwater hydrol ogy The nonlinear system is written in a fractional ow formulation i e in terms of a saturation and a global pressure The saturation equation is approximated by a nite element method while the pressure equation is trea...