Robust Stabilization of Fractional-order Interval Systems via Dynamic Output Feedback: An LMI Approach
For control engineers dealing with uncertain fractional-order systems, this work provides a systematic LMI framework for robust stabilization, though it is an incremental extension of existing LMI methods to fractional-order interval systems.
This paper presents LMI-based sufficient conditions for designing robust dynamic output feedback controllers that asymptotically stabilize fractional-order interval systems with order 0<α<2, enabling low-order controller design. Numerical examples demonstrate the effectiveness of the approach.
This paper addresses the problem of robust dynamic output stabilization of FO-LTI interval systems with the fractional order 0<α<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.