Bilinear systems are a special class of nonlinear systems. With the bilinear part in the state-equation, bilinear systems are more suitable than linear systems for the approximation of nonlinear systems. However, a series approach connects bilinear systems strongly to linear systems. This enables the possibility to adapt the system theory and model reduction methods for linear systems to bilinear systems.
In this sense, we start by investigating the Volterra series representation of bilinear systems and develop a criterion for convergence. Through this kind of representation we are able to define transfer functions for bilinear systems.
Subsequent, we discuss system-theoretic concepts of bilinear systems. Thereby, we especially examine BIBO stability, controllability, observability and bilinear system norms. This establishes the needed requirements for model reduction.
Regarding model reduction, we first discuss the basic concepts as well as subsystem interpolation. Following, we gain in-depth knowledge about Volterra series interpolation. In this context, we discuss different aspects of implementation of this framework. After that, we extend the multipoint Volterra series interpolation to match higher order moments and upgrade the previously introduced implementations for this. As a last point of model reduction we discuss an algorithm, which computes an $\mathcal{H}_2$-optimal model. Concluding, we test the theoretic concepts using bilinear benchmark models.
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Bilinear systems are a special class of nonlinear systems. With the bilinear part in the state-equation, bilinear systems are more suitable than linear systems for the approximation of nonlinear systems. However, a series approach connects bilinear systems strongly to linear systems. This enables the possibility to adapt the system theory and model reduction methods for linear systems to bilinear systems.
In this sense, we start by investigating the Volterra series representation of bilinear...
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