Stability and Control Design for Time-Varying Systems with Time-Varying Delays using a Trajectory-Based Approach

Frédéric Mazenc 1 Michael Malisoff 2 Silviu-Iulian Niculescu 3
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
2 LSU Mathematics - Department of Mathematics [Baton Rouge]
3 L2S - Laboratoire des signaux et systèmes
Abstract : A recent work by Mazenc and Malisoff provides a trajectory-based approach for proving stability of time-varying systems with time-varying delays. Here, we provide several significant applications of their approach. In two results, we use a Lyapunov function for a corresponding un-delayed system to provide a new method for proving stability of linear continuous-time time-varying systems with bounded time-varying delays. We allow uncertainties in the coefficient matrices of the systems. Our main results use upper bounds on an integral average involving the delay. The results establish input-to-state stability with respect to disturbances. We also provide a novel reduction model approach that ensures global exponential stabilization of linear systems with a time-varying pointwise delay in the input, which allows the delay to be discontinuous and uncertain. Finally, we provide an alternative to the reduction model method, based on a different dynamic extension. Our examples demonstrate the usefulness of our findings in several settings.
Keywords : 93Dxx stability I Introduction delay reduction approach time-varying stability AMS subject classifications 93Cxx
Document type :
Journal articles
Complete list of metadatas

Cited literature [48 references]  Display  Hide  Download
https://hal.inria.fr/hal-01660100
Contributor : Frederic Mazenc <>
Submitted on : Monday, December 11, 2017 - 5:16:58 PM
Last modification on : Friday, August 2, 2019 - 11:46:02 AM
Long-term archiving on : Monday, March 12, 2018 - 12:20:08 PM

File

siampresquefinalfmsinmm.pdf
Files produced by the author(s)

Identifiers

Collections

L2S | INRIA | CENTRALESUPELEC | SUP_LSS | INRIA2017 | SUP_SYSTEMES | UNIV-PARIS-SACLAY

Citation

Frédéric Mazenc, Michael Malisoff, Silviu-Iulian Niculescu. Stability and Control Design for Time-Varying Systems with Time-Varying Delays using a Trajectory-Based Approach. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (1), pp.533 - 556. ⟨10.1137/15M1027838⟩. ⟨hal-01660100⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

310

Files downloads

206

Contact


archive-ouverte@inria.fr