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

Jerzy Baranowski, Marta Zagorowska, Waldemar Bauer, Tomasz Dziwinski, Pawel Piatek


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.



Command and control systems; stability; stability criteria; Lyapunov methods; fractional calculus.

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Print ISSN: 1392-1215
Online ISSN: 2029-5731