Nonlinear Systems of Fractional-Orders

The global stability of continuous-time multi-input multi-output nonlinear feedback systems with different fractional orders and interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of this class of positive nonlinear systems are established. Sufficient conditions for the exponential decay of processes in fractional nonlinear systems are given. Procedures for computation of a gain matrix characterizing the class of nonlinear elements are proposed and illustrated by examples.

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Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2021-0040 ◽

2021 ◽

Vol 24 (3) ◽

pp. 950-962

Author(s):

Tadeusz Kaczorek ◽

Łukasz Sajewski

Keyword(s):

Nonlinear Systems ◽

Global Stability ◽

Positive Feedback ◽

Continuous Time ◽

Sufficient Conditions ◽

Stability Conditions ◽

Nonlinear Feedback ◽

Feedback Systems ◽

Fractional Orders ◽

Nonlinear Feedback Systems

Abstract The global stability of continuous-time fractional orders nonlinear feedback systems with positive linear parts and interval state matrices is investigated. New sufficient conditions for the global stability of this class of positive feedback nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple example.

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A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

Mathematical Problems in Engineering ◽

10.1155/2021/7844544 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Dorsaf Etlili ◽

Atef Khedher ◽

Ayachi Errachdi

Keyword(s):

Numerical Simulation ◽

Nonlinear Systems ◽

Fractional Order ◽

Caputo Derivative ◽

High Gain ◽

Estimation Problem ◽

Fractional Order Systems ◽

High Gain Observer ◽

Fractional System ◽

Fractional Orders

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.

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