Improved quasi‐uniform stability criterion of fractional‐order neural networks with discrete and distributed delays

Abstract

This article mainly investigates the quasi‐uniform stability of fractional‐order neural networks with time discrete and distributed delays (FONNDDDs). First, a novel fractional‐order Gronwall inequality with discrete and distributed delays (FOGIDDDs) is established; it can be used to study the stability of a variety of fractional‐order systems with discrete and distributed delays (FOSDDDs). Second, on the basis of this inequality and Leray‐Schauder alternative theorem, the existence and uniqueness results for the FONNDDDs are proved. Third, an improved criterion for the quasi‐uniform stability of FONNDDDs is obtained in terms of this inequality. Ultimately, one numerical example is provided to expound the effectiveness and the superiority of the proposed result.

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

“…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]. FO systems are also very helpful to describe the physical and dynamic processes of the problems more accurately in engineering fields because many practical problems must consider the FO dynamics behavior contained in the constituent materials [38].…”

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

“…Fractional calculus extends integer calculus, one of the most influential mathematical tools worldwide [18][19][20][21]. Due to their memory properties, FO systems can better explain specific actual system models [22][23][24][25], such as control processing [26], circuit systems [27], electrical noises [28], and semi-crystalline polymers [29], than integer-order systems. FO systems are also advantageous to describe the physical and dynamic processes of the problems more precisely in engineering fields because many practical problems must involve the FO dynamics behavior embedded in the constituent materials [30].…”

Novel admissibility and robust stabilization conditions for fractional‐order singular systems with polytopic uncertainties

“…In recent years, fractional-order systems (FOSs) have attracted increasing interest of scholars [1][2][3][4][5][6][7][8][9][10] as they can describe the physical phenomena in nature more accurately such as electrical circuit models [11], supercapacitor models [12], neural networks [13,14], epidemic diseases prediction [15], and so on [16,17]. The main reasons lie in that the FOSs can describe the history-dependent development process of systems and have stronger global relevance than integer-order systems [18].…”