Partial practical stability for fractional‐order nonlinear systems

Abstract

In this paper, stability analysis which ensures the convergence of a part of the solutions towards a ball of a class of fractional‐order nonlinear systems is described. Using the Lyapunov‐like functions, such nonlinear systems depending on a small parameter is studied, and such practical stability is ensured. Numerical examples are given to illustrate the validity of the proposed theoretical results as well as a real application to a class of cobweb models.

H∞ filtering for continuous fractional‐order 2D Roesser model: The 0<α≤1 case

“…Proof. The general idea of the proof of Theorem 2 is to transform the LMI (28) into the form of LMI (27) in Corollary 1. Define  =  −1 , premultiplying and postmultiplying Σ by…”

“…The FO 2D Fornasini-Marchesini models and Roesser models have become a research hotspot recently [23][24][25]. Fractional calculus is the extension of integer calculus, which is one of the most powerful mathematical tools around the world [26][27][28][29][30]. Different from integer order systems, FO systems can describe some practical system models more accurately due to their memory property [31][32][33], for example, control processing [34], circuit systems [35], electrical noises [36], and semicrystalline polymers [37].…”

Design of Polynomial Observer-Based Control of Fractional-Order Power Systems

“…The rapid development of FC has attracted many researchers to investigate the stability analysis of F-OS, leading to the development of specialized techniques and methodologies. Researchers have explored stability criteria, Lyapunov functions [22][23][24][25], and stability regions in the fractional-order space [26]. As the understanding of stability in F-OS continues to evolve, it has enriched both the theoretical foundations of mathematics and practical applications across disciplines, like control theory, physics, engineering, biology, and more [27].…”

Robust ∞ model reduction for the continuous fractional‐order two‐dimensional Roesser system: The 0 < ε ≤ 1 case

“…This manuscript focuses on the $$$ {H}_{\infty } $$$ model reduction problem for continuous FO 2D Roesser system with the FO $$$ 0&lt;\varepsilon \le 1 $$$ and the robust $$$ {H}_{\infty } $$$ model reduction problem for continuous FO 2D Roesser system with the FO $$$ 0&lt;\varepsilon \le 1 $$$ with polytopic uncertainties. Fractional calculus extends integer calculus, one of the most influential mathematical tools worldwide [18–21]. Due to their memory properties, FO systems can better explain specific actual system models [22–25], such as control processing [26], circuit systems [27], electrical noises [28], and semi‐crystalline polymers [29], than integer‐order systems.…”