The structure of the controllable set for multimodal systems

Conner, Luther T.; Stanford, David P.

doi:10.1016/0024-3795(87)90033-4

Cited by 24 publications

(12 citation statements)

References 6 publications

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“…If the temporal sequences can be designed arbitrarily without a specified order, that is, the switching between any two (A i , B i ) and (A j , B j ) is allowable (i, j = 1, ..., N ), we obtain the switched systems [13]. More precisely, a switched system is described by the following equation [16]…”

Section: Model Description and Definitionsmentioning

confidence: 99%

“…As above, we denote those generic numbers by grankR and gdim Ω, respectively. We remark that [13] has decomposed the reachable set of a discretetime switched system into the union of some 'maximal' subspaces. However, such a decomposition is not always possible and is not suitable for the generic analysis.…”

Section: It Turns Out That If (mentioning

confidence: 99%

“…On the other hand, from the system theory, temporal networks can be seen as switched systems when the switching sequence is predetermined. In the context of hybrid systems and switched systems, controllability and reachability have been extensively studied [13,14,15,16,17]. When the switching law can be designed arbitrarily, it is found the reachable and controllable set of switched continuous-time systems are subspaces of the total space, and the complete characterizations were given in [16].…”

Section: Introductionmentioning

confidence: 99%

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On the Reachability and Controllability of Temporal Continuous-Time Linear Networks: A Generic Analysis

Zhang¹,

Xia²,

Wang³

2023

Preprint

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Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of temporal continuous-time linear networks from a generic viewpoint, where only the zero-nonzero patterns of subsystem matrices are known. We demonstrate that the reachability and controllability on a single temporal sequence are generic properties with respect to the parameters of subsystem matrices and the time durations of subsystems. We then give explicit expressions for the minimal subspace that contains the reachable set across all possible temporal sequences (called overall reachable set). It is found that verifying the structural reachability/controllability and structural overall reachability are at least as hard as the structural target controllability verification problem of a single system, implying that finding verifiable conditions for them is hard. Graph-theoretic lower and upper bounds are provided for the generic dimensions of the reachable subspace on a single temporal sequence and of the minimal subspace that contains the overall reachable set. These bounds extend classical concepts in structured system theory, including the dynamic graph and the cactus, to temporal networks, and can be efficiently calculated using graph-theoretic algorithms. Finally, applications of the results to the structural controllability of switched linear systems are discussed.

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Section: Model Description and Definitionsmentioning

confidence: 99%

Section: It Turns Out That If (mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Reachability and Controllability of Temporal Continuous-Time Linear Networks: A Generic Analysis

Zhang¹,

Xia²,

Wang³

2023

Preprint

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“…It is shown that this set (termed controllable set in [12]) is a subspace under certain hypothesis, but not always the case in general. Some further extension of this work can be found in [3], where the controllable set as the union of its maximal components was investigated.…”

Section: Introductionmentioning

confidence: 99%

Reachability and controllability of switched linear discrete-time systems

Sun

Lee

2001

IEEE Trans. Automat. Contr.

172

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“…For a switched linear discrete-time control system, the controllable set is not a subspace but a countable union of subspaces in general case (Stanford & Conner 1980, Conner & Stanford 1987. For a switched linear continuous-time control system, the controllable set is an uncountable union of subspaces (Sun & Zheng 2001).…”

Section: Introductionmentioning

confidence: 99%