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Analysis and Design of Robust Controller for Polynomial Fractional Differential Systems Using Sum of Squares

journal contribution
posted on 2024-02-07, 04:28 authored by Hassan Yaghoubi, Assef Zare, Roohallah AlizadehsaniRoohallah Alizadehsani
This paper discusses the robust stability and stabilization of polynomial fractional differential (PFD) systems with a Caputo derivative using the sum of squares. In addition, it presents a novel method of stability and stabilization for PFD systems. It demonstrates the feasibility of designing problems that cannot be represented in LMIs (linear matrix inequalities). First, sufficient conditions of stability are expressed for the PFD equation system. Based on the results, the fractional differential system is Mittag–Leffler stable when there is a polynomial function to satisfy the inequality conditions. These functions are obtained from the sum of the square (SOS) approach. The result presents a valuable method to select the Lyapunov function for the stability of PFD systems. Then, robust Mittag–Leffler stability conditions were able to demonstrate better convergence performance compared to asymptotic stabilization and a robust controller design for a PFD equation system with unknown system parameters, and design performance based on a polynomial state feedback controller for PFD-controlled systems. Finally, simulation results indicate the effectiveness of the proposed theorems.

History

Journal

Axioms

Volume

11

Article number

623

Pagination

1-13

Location

Basel, Switzerland

ISSN

2075-1680

eISSN

2075-1680

Language

eng

Publication classification

C1 Refereed article in a scholarly journal

Issue

11

Publisher

MDPI

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