Robust Stabilization of Fractional-order Interval Systems via Dynamic Output Feedback: An LMI Approach

TL;DR

This paper develops an LMI-based method for designing robust dynamic output feedback controllers that stabilize fractional-order interval systems, ensuring robustness against uncertainties with minimal controller order.

Contribution

It introduces a new LMI approach for robust stabilization of fractional-order interval systems using low-order dynamic output feedback controllers.

Findings

Successfully stabilizes fractional-order interval systems.

Provides LMI conditions for controller design.

Demonstrates effectiveness through numerical examples.

Abstract

This paper addresses the problem of robust dynamic output stabilization of FO-LTI interval systems with the fractional order 0<{\alpha}<2, in terms of linear matrix inequalities (LMIs). Our purpose is to design a robust dynamic output feedback controller that asymptotically stabilizes interval fractional-order linear time-invariant (FO-LTI) systems. Sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. The LMI-based procedures of designing robust stabilizing controllers are preserved in spite of the complexity of assuming the most complete model of linear controller, with direct feedthrough parameter. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results. Keywords: Fractional-order system, interval uncertainty, linear matrix inequality (LMI), robust stabilization, dynamic output feedback.