<abstract xmlns="http://www.w3.org/1999/xhtml">The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics <italic>u</italic> = <italic>f</italic>(<italic>e</italic>) of the nonlinear parts satisfy the condition <italic>k</italic>1<italic>e</italic> ≤ <italic>f</italic>(<italic>e</italic>) ≤ <italic>k</italic>2<italic>e</italic> for some positive <italic>k</italic>1 and <italic>k</italic>2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1<italic>/k</italic>1, −1<italic>/k</italic>2).</abstract>

The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1, −1/k2).

Global Stability of Nonlinear Feedback Systems with Fractional Positive Linear Parts

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is...

Global Stability of Nonlinear Feedback Systems with Fractional Positive Linear Parts

Published Online: Sep 29, 2020

Page range: 493 - 499

Received: Oct 11, 2019

Accepted: May 13, 2020

DOI: https://doi.org/10.34768/amcs-2020-0036

Keywords
global, stability, fractional, nonlinear, feedback, positive, system

© 2020 Tadeusz Kaczorek, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Global Stability of Nonlinear Feedback Systems with Fractional Positive Linear Parts

Published Online: Sep 29, 2020

Page range: 493 - 499

Received: Oct 11, 2019

Accepted: May 13, 2020

DOI: https://doi.org/10.34768/amcs-2020-0036

Keywordsglobal, stability, fractional, nonlinear, feedback, positive, system

© 2020 Tadeusz Kaczorek, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
global, stability, fractional, nonlinear, feedback, positive, system