Fabian R. Wirth

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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)
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 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)
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)
In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a(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)
We study structural properties of linear time-varying discrete-time systems. At rst an associated system on projective space is introduced as a basic tool to understand the linear dynamics. We study controllability properties of this system, and characterize in particular the control sets and their cores. Suucient conditions for an upper bound on the number(More)