LMI-based robust stability and stabilization analysis of fractional-order interval systems with time-varying delay

TL;DR

This paper develops LMI-based methods for analyzing and stabilizing fractional-order interval systems with time-varying delays, providing practical conditions for robust stability and controller design.

Contribution

It introduces new LMI-based stability and stabilization criteria for fractional-order systems with interval uncertainties and delays, including a controller design approach with minimal order.

Findings

The proposed LMIs effectively verify stability and stabilization.

Numerical examples confirm the practicality of the methods.

The approach simplifies controller design for complex fractional systems.

Abstract

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization theorem is also included, where sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. Utilizing efficient lemmas, the stability and stabilization theorems are proposed in the form of LMIs, which is more suitable to check due to various existing efficient convex optimization parsers and solvers. Finally, two numerical examples have shown the effectiveness of our results.