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.
Bibliographical noteFunding 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:,firstname.lastname@example.org).
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- Hybrid invariant zeros
- hybrid systems
- strong detectability
- strong observability