Detectability and observer design for switched differential–algebraic equations

Tanwani, A. & Trenn, S., Jan-2019, In : Automatica. 99, p. 289-300 12 p.

Research output: Contribution to journalArticleAcademicpeer-review

Copy link to clipboard


  • Final aut- Detectability and observer design for switched differential–algebraic equations-

    Final author's version, 524 KB, PDF document

    Embargo ends: 14/11/2020

    Request copy

  • Detectabilityandobserverdesignforswitcheddifferential–algebraic equations

    Final publisher's version, 652 KB, PDF document

    Request copy


This paper studies detectability for switched linear differential–algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.
Original languageEnglish
Pages (from-to)289-300
Number of pages12
Early online date14-Nov-2018
Publication statusPublished - Jan-2019


  • Switched systems, Differential–algebraic equations, Detectability, Observer design, State estimation, Asymptotic convergence, TO-STATE STABILITY

ID: 67592300