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- Roman Geiselhart, Mircea Lazar, Fabian R. Wirth
- IEEE Transactions on Automatic Control
- 2015

This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is thatâ€¦ (More)

- Roman Geiselhart, Fabian R. Wirth
- SIAM J. Control and Optimization
- 2016

In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gainâ€¦ (More)

- Roman Geiselhart, Rob H. Gielen, Mircea Lazar, Fabian R. Wirth
- Systems & Control Letters
- 2014

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discreteâ€“time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function.â€¦ (More)

- Roman Geiselhart, Fabian R. Wirth
- IEEE Conference on Decision and Control andâ€¦
- 2011

We provide a homotopy algorithm that computes a decay point of a monotone operator, i.e., a point whose image under the monotone operator is strictly smaller than the preimage. For this purpose weâ€¦ (More)

- Roman Geiselhart, Fabian R. Wirth
- SIAM J. Control and Optimization
- 2015

In the analysis of large-scale interconnected systems, small-gain conditions may be used to derive stability properties of the overall system. This paper investigates the question of how largeâ€¦ (More)

- W. P. M. H. Heemels, Dominicus Paulus Borgers, Victor Sebastiaan Dolk, Roman Geiselhart, Stefan H. J. Heijmans
- 2016 European Control Conference (ECC)
- 2016

In this tutorial presentation we focus on the construction of Lyapunov or storage functions for large-scale networked control systems (NCSs) in which sensors, controllers and actuators are connectedâ€¦ (More)

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function.â€¦ (More)

- Roman Geiselhart, Rob H. Gielen, Mircea Lazar, Fabian R. Wirth
- NOLCOS
- 2013

This paper makes use of the concept of a finiteâ€“time Lyapunov function to derive a nonâ€“ conservative small-gain theorem for stability analysis of interconnected discreteâ€“time nonlinear systems.â€¦ (More)

In this paper we make use of the alternative converse Lyapunov theorem presented in [1] for specific classes of systems. We show that the developed converse Lyapunov theorem can be used to establishâ€¦ (More)

- Navid Noroozi, Roman Geiselhart, Lars Grüne, Björn S. Rüffer, Fabian R. Wirth
- IEEE Transactions on Automatic Control
- 2018

This paper presents a unification and a generalization of the small-gain theory subsuming a wide range of existing small-gain theorems. In particular, we introduce small-gain conditions that areâ€¦ (More)

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