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On the prescribed-time attractivity and frozen-time eigenvalues of linear time-varying systems

Shakouri, A ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1016/j.automatica.2022.110173
  3. Publisher: Elsevier Ltd , 2022
  4. Abstract:
  5. A system is called prescribed-time attractive if its solution converges at an arbitrary user-defined finite time. In this note, necessary and sufficient conditions are developed for the prescribed-time attractivity of linear time-varying (LTV) systems. It is proved that the frozen-time eigenvalues of a prescribed-time attractive LTV system have negative real parts when the time is sufficiently close to the convergence moment. This result shows that the ubiquitous singularity problem of prescribed-time attractive LTV systems can be avoided without instability effects by switching to the corresponding frozen-time system at an appropriate time. Consequently, it is proved that the time-varying state-feedback gain of a prescribed-time controller, designed for an unknown linear time-invariant system, approaches the set of stabilizing constant state-feedback gains. © 2022 Elsevier Ltd
  6. Keywords:
  7. Frozen-time eigenvalues ; Invariance ; Linear time-invariant system ; State feedback ; Time varying control systems ; Attractivity ; Eigen-value ; Finite-time ; Frozen-time eigenvalue ; Linear time-varying systems ; Prescribed-time attractivity ; Prescribed-time control ; State feedback gain ; Time control ; Time-varying systems ; Eigenvalues and eigenfunctions
  8. Source: Automatica ; Volume 140 , 2022 ; 00051098 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0005109822000188