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- Robert Shorten, Fabian R. Wirth, Oliver Mason, Kai Wulff, Christopher K. King
- SIAM Review
- 2007

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)

- Fabian Wirth
- 2003

- Sergey Dashkovskiy, Björn Rüffer, Fabian R. Wirth
- MCSS
- 2007

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear… (More)

- Fabio Camilli, Lars Grüne, Fabian R. Wirth
- SIAM J. Control and Optimization
- 2001

We present a generalization of Zubov's method to perturbed differential equations. The goal is to characterize the domain of attraction of a set which is uniformly locally asymptotically stable under all admissible time varying perturbations. We show that in this general setting the straightforward generalization of the classical Zubov's equations has a… (More)

We consider a network consisting of n interconnected nonlinear subsystems. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. We use a gain matrix to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, we… (More)

- Robert Shorten, Fabian R. Wirth, Douglas J. Leith
- IEEE/ACM Transactions on Networking
- 2006

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)

- Andrew Paice, Fabian Wirth
- 1998

We consider a perturbed nonlinear system with a xed point that is invariant under all perturbations. Under the assumption that this xed point is locally exponentially stable for the unperturbed system we propose a method for the approximation of the robust domain of attraction, that is, the set of points that are attracted to the xed point under all… (More)

- Nicola Guglielmi, Fabian R. Wirth, Marino Zennaro
- SIAM J. Matrix Analysis Applications
- 2005

- Robert Shorten, Christopher K. King, Fabian R. Wirth, Douglas J. Leith
- Automatica
- 2007

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.

- Fabian R. Wirth
- SIAM J. Control and Optimization
- 2005

We study families of linear time-varying systems, where time-variations have to satisfy restrictions on the dwell time, that is on the minimum distance between discontinuities, as well as on the derivative in between dis-continuities. Such classes of systems may be formulated as linear flows on vector bundles. The main objective of the paper is to construct… (More)