Stability of fractional‐order nonlinear systems by Lyapunov direct method

By Hoang The Tuan, Hieu Minh Trinh. IET Control Theory & Applications, 2017

117 citations recorded by the source corpus.

In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption on the existence of derivative of pseudo-states. Second, we establish fractional Lyapunov functions to fractional-order systems without the assumption on the global existence of solutions. Our theorems fill the gaps and strengthen results in some existing papers.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e0ccd025b7ef2cffea31518362489001988fe97b

How researchers see this paper

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In Control and Systems Engineering

1. Nguyen Dinh Cong
2. Hieu Minh Trinh
3. Hoang The Tuan

In Modeling and Simulation

1. Nguyen Dinh Cong
2. Hieu Minh Trinh
3. Hoang The Tuan

In Numerical Analysis

1. Nguyen Dinh Cong
2. Hieu Minh Trinh
3. Hoang The Tuan

Citations in the corpus

• On asymptotic properties of solutions to fractional differential equations (2018, methodology): “However, in those papers there are some shortcomings of that approach and some flaws in the proofs, which were shown in [30].”