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arXiv · 1212.1839

On Structured Realizability and Stabilizability of Linear Systems

Laurent Lessard·Maxim Kristalny·Anders Rantzer
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Abstract

We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the associated graph. In this paper, we demonstrate that not every structured transfer matrix has a structured realization and we reveal the practical meaning of this fact. We also uncover a close connection between the structured realizability of a plant and whether the plant can be stabilized by a structured controller. In particular, we show that a structured stabilizing controller can only exist when the plant admits a structured realization. Finally, we give a parameterization of all structured stabilizing controllers and show that they always have structured realizations.

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Laurent Lessard, Maxim Kristalny, Anders Rantzer. 2012-12-08. On Structured Realizability and Stabilizability of Linear Systems. https://arxiv.org/abs/1212.1839

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