Abstract
This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.
Highlights
In recent years, fractional calculus deals with derivatives and integrations of arbitrary order [1, 2] and has found many applications in different areas of physics, applied mathematics, and technology
Fractional calculus deals with derivatives and integrations of arbitrary order [1, 2] and has found many applications in different areas of physics, applied mathematics, and technology. Due to their characterization by fractional-order equations, several studies show that certain dynamics systems are governed by differential equations with noninteger derivatives. e use of classical models based on an integer derivation is not appropriate. erefore, models based on noninteger differential equations have been developed
The heat transfer process modelling for photovoltaic/thermal hybrid system [5], which is defined by heterogeneous media due to the multilayers that make up the system, can be characterized by a fractional-order partial differential equation. e applications are numerous, whether in electricity, chemistry, or signal processing [6,7,8,9]
Summary
Fractional calculus deals with derivatives and integrations of arbitrary order [1, 2] and has found many applications in different areas of physics, applied mathematics, and technology Due to their characterization by fractional-order equations, several studies show that certain dynamics systems are governed by differential equations with noninteger derivatives. Mathematical Problems in Engineering proposed the indirect application of Lyapunov to find LMIbased nonfragile fractional-order observer gain for a class of Lipschitz nonlinear systems using continuous frequency distribution. In consideration of its performance and its robustness to uncertainty and perturbations, the sliding mode observer is attracting the interest of researchers in fractional-order systems Most of these approaches of fractional-order nonlinear systems are based on the Lyapunov stability [25,26,27]. A high-gain observer is proposed for fractional-order nonlinear systems.
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