Pseudo-Lyapunov methods for Grünwald-Letnikov and initialized fractional systems
Corresponding Author
Javier A. Gallegos
Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile
Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Av. Vicuña Mackenna 4860, Chile
Correspondence
Javier A. Gallegos, Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile.
Email: [email protected]
Communicated by: R. Picard
Search for more papers by this authorNorelys Aguila-Camacho
Department of Electricity, Universidad Tecnológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago, Chile
Search for more papers by this authorCorresponding Author
Javier A. Gallegos
Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile
Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Av. Vicuña Mackenna 4860, Chile
Correspondence
Javier A. Gallegos, Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile.
Email: [email protected]
Communicated by: R. Picard
Search for more papers by this authorNorelys Aguila-Camacho
Department of Electricity, Universidad Tecnológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago, Chile
Search for more papers by this authorAbstract
This paper presents reduced-order methods to study the stability of initialized or Grünwald-Letnikov fractional nonlinear systems. It is shown that the initialization procedure must be formalized by introducing a class of systems, and the corresponding stability analysis must be established for each element of that class. The main features obtained using this novel approach are (a) the requirements for stability are imposed directly on the equations of the system and involve only finite-dimensional variables; (b) the conclusions are asserted on the variables of interest; (c) the method can be extended in several ways, including multi-order systems. Illustrative examples, including an application in adaptive control, are finally presented to convey the usefulness of our approach.
CONFLICT OF INTEREST
This work does not have any conflicts of interest.
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