On observer-based control of one-sided Lipschitz ω-tempered fractional-order systems under input saturation

Soumaya Afli ^[1] ; Assaad Jmal ^[1] ; Omar Naifar ^[2]
1. [1] University of Sfax
  
  University of Sfax
  
  Túnez
2. [2] University of Kairouan
  
  University of Kairouan
  
  Túnez
Localización: Métodos numéricos para cálculo y diseño en ingeniería: Revista internacional, ISSN 0213-1315, Vol. 41, Nº 4, 2025
Idioma: español
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Resumen
- This paper addresses the critical challenge of observer-based control for one-sided Lipschitz (OSL) nonlinear systems governed by tempered fractional-order dynamics under input saturation constraints. We introduce a novel stability framework combining ω-tempered Caputo derivatives with Mittag-Leffler stability theory, enabling significantly faster exponential error decay compared to classical fractional operators. The proposed methodology features three key innovations: (1) a tempered Mittag-Leffler stability theorem incorporating sector-bounded saturation nonlinearities, (2) linear matrix inequality (LMI) conditions accommodating arbitrary OSL constants (ρ∈ R), and (3) a Cone Complementary Linearization (CCL) algorithm resolving gain synthesis challenges in tempered fractional systems. Numerical validation demonstrates 62% faster convergence than classical fractional approaches while maintaining saturation constraints. The CCL algorithm provides guaranteed convergence with computational efficiency, overcoming initialization sensitivity through regularization techniques.