Non‐fragile H_∞ observer for Lipschitz conformable fractional‐order systems

Abstract

The issue of designing simultaneously robust and non‐fragile observers for the classical integer‐order systems has been widely investigated in the literature. Yet, there are just some few works that have tackled the same problem for non‐integer‐order systems. Moreover, the conformable derivative is an interesting concept that has been introduced by some researchers in the last decade. This new derivative presents some advantageous mathematical properties, compared with older concepts. In this paper, and motivated by these facts, the authors suggest a first scheme to design observers, which are simultaneously robust and non‐fragile, for Lipschitz nonlinear conformable fractional‐order systems. The H∞ performance theory is used for that purpose. The efficiency of the developed approach is confirmed through simulations for a numerical example.

Global Practical Conformable Stabilization by Output Feedback for a Class of Nonlinear Fractional‐Order Systems

“…Additionally, the studies show multiple instances of the diffusion equation solution being unique in [32]. Some further additional efforts to the conformable derivative are recently done by researchers, for example, the multiagent systems with impulsive control protocols [33], numerical methods [34], time power-based grey model [35], multivariate grey system model [36], controllability and observability [37], the Barbalat lemma [38], and H∞ observers [39].…”

Set‐membership state estimation for delayed switched systems with fading measurement and interval uncertainty

“…For different noise types, scholars have proposed different state estimation algorithms, such as the Kalman filter, 13,14 $$$ {H}_{\infty } $$$ state estimation, 15,16 recursive filter, 17–19 and so forth. The Kalman filter and $$$ {H}_{\infty } $$$ state estimation are applied to random systems with known noise statistical properties and systems with limited noise energy, respectively.…”

A Robust and Non-Fragile Observer Design for Nonlinear Fractional-Order Systems

“…The proof is now complete. The article[26] makes a similar development in the context of conformable fractional order systems.…”