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    Herdability of Linear Systems Based on Sign Patterns and Graph Structures

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    Type
    Preprint
    Authors
    Ruf, Sebastian F
    Egerstedt, Magnus
    Shamma, Jeff S. cc
    KAUST Department
    Electrical Engineering Program
    Center of Excellence for NEOM Research
    Date
    2019-04-17
    Permanent link to this record
    http://hdl.handle.net/10754/660696
    
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    Abstract
    We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on herdability of a continuous time, linear time invariant system are presented. These show that the herdability of a linear system can be determined based on certain matrices, such as the controllability matrix, which arise in the study of controllability of linear systems. Second, the relationship between the sign pattern of the underlying graph structure of a system and the herdability properties of the system is investigated. In doing so the notion of sign herdability is introduced which captures classes of systems whose sign pattern determines their herdability. We identify a set of conditions, first on the sign pattern of the controllability matrix and then on the underlying graph structure, that ensure that the system is sign herdable.
    Publisher
    arXiv
    arXiv
    1904.08778
    Additional Links
    https://arxiv.org/pdf/1904.08778
    Collections
    Preprints; Electrical Engineering Program

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