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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(More)
We present a result on the existence of a common quadratic Lyapunov function for a pair of linear time-invariant systems. We show that this result charac-terises, generalises, and provides new perspectives on several well-known stability results. In particular, new time-domain formulations of the Circle Criterion and Meyer's extension of the KYP lemma are(More)
In this paper, we present experimental results evaluating the performance of the scalable-TCP, HS-TCP, BIC-TCP, FAST-TCP, and H-TCP proposals in a series of benchmark tests. In summary, we find that both Scalable-TCP and FAST-TCP consistently exhibit substantial unfairness, even when competing flows share identical network path characteristics.(More)
It was recently conjectured that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching. In this paper we show that: (i) this conjecture is true for systems constructed from a pair of second order Metzler(More)
—Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. Ideally, it is desirable that a dynamic Takagi-Sugeno fuzzy model should give accurate global non-linear prediction and at the same time that its local models are close approximations to the local linearizations of the(More)
We study communication networks that employ drop-tail queueing and Additive-Increase Multiplicative-Decrease (AIMD) congestion control algorithms. It is shown that the theory of nonnegative matrices may be employed to model such networks. In particular, important network properties, such as: 1) fairness; 2) rate of convergence; and 3) throughput, can be(More)
In this report the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a(More)
In this paper we study communication networks that employ drop-tail queueing and additive-increase multiplicative-decrease (AIMD) congestion control algorithms. We show that the theory of non-negative matrices may be employed to model such networks and to derive basic theorems concerning their behaviour. ᭧ 2007 Published by Elsevier Ltd.
—Delay-based TCP variants have attracted a large amount of attention in the networking community because of their ability to efficiently use network resources, control queuing delays, exhibit virtually zero packet loss, etc. One major issue that discourages the wider deployment of delay-based TCP variants is their inability to co-exist fairly with standard(More)