Linear Hybrid Systems with Periodic Jumps: A Notion of Strong Observability and Strong Detectability

Hector Rios, Jorge Davila, Andrew R. Teel

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13 Scopus citations


In this paper, two important structural properties, i.e., strong observability and strong detectability, are introduced for linear hybrid systems with periodic jumps. These properties are characterized in terms of geometric and algebraic conditions over the system matrices. The concepts and characterizations of the weakly unobservable subspace and the hybrid invariant zeros are also introduced, respectively. An algorithm to compute the weakly unobservable subspace is provided. In addition, it is shown that there exists a close relationship between the hybrid invariant zeros and the properties ofstrong observability and strong detectability. Some examples illustrate the proposed properties.

Original languageEnglish
Article number8827648
Pages (from-to)2640-2646
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 2020

Bibliographical note

Funding Information:
Manuscript received April 1, 2019; accepted September 3, 2019. Date of publication September 9, 2019; date of current version May 28, 2020. The work of H. Ríos was supported by CONACYT 270504, J. Davila acknowledges the support from SIP-IPN under grant 20195310, and A.R. Teel was supported by NSF grant ECCS-1508757 and AFOSR grant FA9550-18-1-0246. Recommended by Associate Editor L. Menini. (Corresponding author: Héctor Ríos.) H. Ríos is with the División de Estudios de Posgrado e Investigación, CONACYT-Tecnológico Nacional de México/I.T. La Laguna, C.P. 27000 Torreón, México (e-mail:,

Publisher Copyright:
© 1963-2012 IEEE.


  • Hybrid invariant zeros
  • hybrid systems
  • strong detectability
  • strong observability


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