Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case

Sutrisno Sutrisno*, Stephan Trenn

*Corresponding author for this work

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In this paper, we investigate the observability of singular linear switched systems in discrete time. As a preliminary study, we restrict ourselves to systems with a single switch switching signal, i.e. the system switches from one mode to another mode at a certain switching time. We provide two necessary and sufficient conditions for the observability characterization. The first condition is applied for arbitrary switching time and the second one is for switching times that are far enough from the initial time and the final time of observation. These two conditions explicitly contain the switching time variable that indicates that in general, the observability is dependent on the switching time. However, under some sufficient conditions we provide, the observability will not depend on the switching time anymore. Furthermore, the observability of systems with two-dimensional states is independent of the switching time. In addition, from the example we discussed, an observable switched system can be built from two unobservable modes and different mode sequences may produce different observability property; in particular, swapping the mode sequence may destroy observability.
Original languageEnglish
Title of host publication2021 European Control Conference (ECC)
Place of PublicationDelft
Number of pages5
ISBN (Electronic)978-9-4638-4236-5
ISBN (Print)978-1-6654-7945-5
Publication statusPublished - 29-Jun-2021
EventEuropean Control Conference 2021 - Rotterdam, Netherlands
Duration: 29-Jun-20212-Jul-2021


ConferenceEuropean Control Conference 2021
Abbreviated titleECC21
Internet address


  • Switched systems
  • Dingular systems
  • Observability
  • Discrete-time

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