The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities , and to review some problems that remain open. An important contribution of our work is to bring to...

This report investigates the dynamics of RED queue management in the presence of FTP and Web-like TCP reno flows for scenarios with homogeneous and heterogeneous round trip times. We systematically derive quantitative guidelines and steady state models how to set the RED-parameters as a function of the scenario parameters bottleneck-bandwidth, round-trip-time, number of TCP flows in order to av...

It was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable Lie algebra possesses a quadratic common Lyapunov function, which implies that the corresponding switched linear system is exponentially stable for arbitrary switching. In this paper we prove that the same properties hold under the weaker condition that the Lie algebra generated by give...

Recent numerical studies in the area of transition to turbulence discovered that the classical plane Couette flow, plane Poiseuille flow, and pipe Poiseuille flow share some universal 3D steady coherent structure in the form of a “streak-roll-critical layer”. As the Reynolds number approaches infinity, the steady coherent structure approaches a 3D limiting shear of the form (U(y, z), 0, 0) in v...

It was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable Lie algebra possesses a quadratic common Lyapunov function, which implies that the corresponding switched linear system is exponentially stable for arbitrary switching. In this paper we prove that the same properties hold under the weaker condition that the Lie algebra generated by give...

There are many different analysis methods for evaluation of complicated socio-economic processes. Banks are important participants of the market. Soundness and stability of banks is difficult to assess because of their complicated internal business structure, intertwined cash flows and strong influence of market conditions on bank’s performance. Multi-criteria methods of evaluation are among ma...

In this paper a description of a certain class of multiloop systems, called the Standard Multiloop Form, is introduced. This description is expressed explicitly in terms of certain scalar subsystems and can be shown to include many of the common descriptions of multiloop systems. The stability criteria presented in this paper involve the individual Nyquist plots of the linear scalar subsystems ...

Strength reduction finite element method (SRFEM) has been widely used to analyze the slope stability. Strength Reduction Factor (SRF) is yielded as the slope Factor Of Safety (FOS) when a running-though shear failure zone comes into being, in which the Plastic Element EQuivalent strain (PEEQ) is employed as the judgment of shear failure initiation in this paper. Moreover, the filed variable is ...

A new variational approach to irreversible thermodynamics has been developed leading to lagrangian equations of evolution. The essential results have been presented recently in the form of a short monograph [l]. Its foundation rests on a fundamental principle of virtual dissipation. Our purpose here is to derive new stability criteria for a steady state evolution based on lagrangian equations i...

The paper is concerned with robust stability criteria for Takagi- Sugeno (T-S) fuzzy systems with distributed delays and time delay in the leakage term. By exploiting a model transformation, the system is converted to one of the neutral delay system. Global robust stability result is proposed by a new Lyapunov-Krasovskii functional which takes into account the range of delay and by making use o...