Applications of Direct Lyapunov Method in Caputo Non-Integer Order Systems

  • Jerzy Baranowski AGH University of Science and Technology
  • Marta Zagorowska AGH University of Science and Technology
  • Waldemar Bauer AGH University of Science and Technology
  • Tomasz Dziwinski AGH University of Science and Technology
  • Pawel Piatek AGH University of Science and Technology
Keywords: Command and control systems, stability, stability criteria, Lyapunov methods, fractional calculus.

Abstract

Paper presents certain properties of Lyapunov direct method for non-integer order systems. Mittag-Leffler stability is defined and its relationship with Lyapunov stability is investigated. General results for Lyapunov functions are presented and a new result allowing constructive stability analysis is proved. Results are illustrated with the examples of stability analysis for problem of cooling, chemical reaction evolution and parametric stability analysis.

DOI: http://dx.doi.org/10.5755/j01.eee.21.2.11505

Published
2015-04-09
Section
AUTOMATION, ROBOTICS