Dynamic robust stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach

TL;DR

This paper develops an LMI-based method for robust stabilization of fractional-order linear systems with nonlinear uncertainties using dynamic output feedback controllers, validated through numerical simulations.

Contribution

It introduces a novel LMI-based approach for designing dynamic output feedback controllers for uncertain fractional-order systems.

Findings

The stabilization conditions are expressed as LMIs.

The method effectively stabilizes systems with nonlinear uncertainties.

Numerical examples confirm the approach's applicability.

Abstract

This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for asymptotically stabilizing such uncertain fractional-order systems is designed. The derived stabilization conditions are in LMI form. Simulation results of two numerical examples illustrate that the proposed sufficient theoretical results are applicable and effective for tackling robust stabilization problems. Keywords: Fractional-order system, nonlinear uncertain parameters, linear matrix inequality (LMI), robust stabilization, dynamic output feedback.