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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)
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)
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)
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)
—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)
—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)
response of the frequency estimation loop and simplified its design. The estimates were unbiased and ripple-free when the signal contained no noise and the parameters of the signal were constant. A modified version of the algorithm provided improvements for situations in which the fundamental component of the signal could become small, or vanish for some(More)
We consider the problem of common linear copositive function existence for positive switched linear systems. In particular, we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time-invariant (LTI) systems. A number of applications of this result are also given.
In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of " linear " stability for the arbitrary switching case; namely,(More)