## Fakultät für Mathematik und Informatik

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- Doctoral Thesis (2)

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#### Keywords

- Akzessibilität (1)
- ISS (1)
- Kommunikationssystem (1)
- Lineares System (1)
- Netzwerk (1)
- Rechnernetz (1)
- Stabilisierung (1)
- Steuerbarkeit (1)
- Steuerbarkeit von Netzwerken (1)
- accessibility (1)

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Several aspects of the control of large-scale systems communicating over digital channels are considered.
In particular, the issue of delay, quantization, and packet loss is addressed with the help of dynamic quantization.
New small-gain results suitable for networked control systems are introduced and it is shown that many of the known small-gain conditions are equivalent.
The issue of bandwidth limitations is addressed with the help of event-triggered control.
A novel approach termed parsimonious triggering is introduced, which helps to rule out the occurrence of an infinite number of triggering events within finite time.
Moreover, the feasibility of the presented approaches is demonstrated by numerical examples.

The subject of this thesis is the controllability of interconnected linear systems, where the interconnection parameter are the control variables. The study of accessibility and controllability of bilinear systems is closely related to their system Lie algebra. In 1976, Brockett classified all possible system Lie algebras of linear single-input, single-output (SISO) systems under time-varying output feedback. Here, Brockett's results are generalized to networks of linear systems, where time-varying output feedback is applied according to the interconnection structure of the network. First, networks of linear SISO systems are studied and it is assumed that all interconnections are independently controllable. By calculating the system Lie algebra it is shown that accessibility of the controlled network is equivalent to the strong connectedness of the underlying interconnection graph in case the network has at least three subsystems. Networks with two subsystems are not captured by these proofs. Thus, we give results for this particular case under additional assumption either on the graph structure or on the dynamics of the node systems, which are both not necessary. Additionally, the system Lie algebra is studied in case the interconnection graph is not strongly connected. Then, we show how to adapt the ideas of proof to networks of multi-input, multi-output (MIMO) systems. We generalize results for the system Lie algebra on networks of MIMO systems both under output feedback and under restricted output feedback. Moreover, the case with generalized interconnections is studied, i.e. parallel edges and linear dependencies in the interconnection controls are allowed. The new setting demands to distinguish between homogeneous and heterogeneous networks. With this new setting only sufficient conditions can be found to guarantee accessibility of the controlled network. As an example, networks with Toeplitz interconnection structure are studied.