The estimation problem for nonlinear systems modeled by conformable derivative: Design and applications

• Published in: Communications in nonlinear science & numerical simulation Vol. 115; p. 106720
• Main Authors: Martínez-Fuentes, O., Tlelo-Cuautle, Esteban, Fernández-Anaya, Guillermo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2022
• Subjects: Chaotic Colpitts oscillator; Fractional-order systems; General conformable exponential observers; General Conformable Fractional Derivative; Lyapunov-like stability methods; Lyapunov-like stability methods; Fractional-order systems; General Conformable Fractional Derivative; Chaotic Colpitts oscillator; General conformable exponential observers
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2022.106720

This work presents an introductory observer theory for nonlinear dynamic systems modeled by the general conformable fractional derivative. General conformable exponential observers are defined, and Lyapunov-like stability methods are developed to design estimation algorithms. Two algorithms are presented to estimate unknown variables on conformable dynamic systems, considering the disturbance-free case, the presence of an input non-vanishing disturbance vector, and the case whit noise signals in the output. The Lyapunov theoretical results are exploited to prove the convergence of the estimation errors. In order to validate the main results, a numerical case is analyzed based on the state estimation of the chaotic Colpitts oscillator. •Classification of conformable observers according to the estimation behavior.•Lyapunov-like theorems to design a more general family of conformable observers.•Two robust algorithms to estimate unknown information based on the Lyapunov analysis.