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Mathematics > Optimization and Control

arXiv:2108.01579 (math)
[Submitted on 3 Aug 2021 (v1), last revised 4 Aug 2021 (this version, v2)]

Title:Algebraic and Graph-Theoretic Conditions for the Herdability of Linear Time-Invariant Systems

Authors:Giulia De Pasquale, Maria Elena Valcher
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Abstract:In this paper we investigate a relaxed concept of controllability, known in the literature as herdability, namely the capability of a system to be driven towards the(interior of the) positive orthant. Specifically, we investigate herdability for linear time-invariant systems, both from an algebraic perspective and based on the graph representing the systems interactions. In addition, we focus on linear state-space models corresponding to matrix pairs (A;B) in which the matrix B is a selection matrix that determines the leaders in the network, and we show that the weights that followers give to the leaders do not affect the herdability of the system. We then focus on the herdability problem for systems with a single leader in which interactions are symmetric and the network topology is acyclic, in which case an algorithm for the leader selection is provided. In this context, under some additional conditions on the mutual distances, necessary and sufficient conditions for the herdability of the overall system are given.
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
Cite as: arXiv:2108.01579 [math.OC]
  (or arXiv:2108.01579v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.01579

Submission history

From: Giulia De Pasquale [view email]
[v1] Tue, 3 Aug 2021 15:41:02 UTC (361 KB)
[v2] Wed, 4 Aug 2021 08:47:20 UTC (178 KB)
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