A novel finite time stability analysis of nonlinear fractional‐order time delay systems: A fixed point approach

Abstract

Finite time stability (FTS) of fractional-order time delayed systems (FOTDSs) has been studied by many researchers based on the Lyapunov functions and Gronwall inequalities. In this paper, we proposed a novel FTS scheme for FOTDSs based on the fixed point theory. By exploiting the fixed point approach, sufficient conditions that guarantee the robust FTS of FOTDSs have been established. Finally, two illustrative examples are presented to validate the main result.

Iterative learning control for impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices

“…Numerous researchers have discussed the data dependence in the theory of differential equations. All kind of stability properties have attracted the attention of many mathematicians, see References 22‐26. Meanwhile, there are some special data dependence in the theory of functional equations such as Ulam–Hyers, Ulam–Hyers–Rassias, and Ulam–Hyers–Bourgin.…”

Convergence on iterative learning control of Hilfer fractional impulsive evolution equations

“…Also, this theory can be developed for discrete system and can be studied further for delay systems. For delay systems, recent article by Ben Makhlouf [31] can be referred.…”

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

“…Later, this concept was developed for FOs and many important results have been addressed for many kinds of FOs by various approaches. [19][20][21][22][23][24][25][26][27][28] By improved fractional-order Gronwall integral inequality with time delays, Du and Lu have solved the problem for some kinds of fractional-order neural networks model such as Hopfield neural networks, 19 and bidirectional associative memory neural networks, 20 fuzzy cellular neural networks, 21 and Cohen-Grossberg memristive neural networks. 22 Feng et al 23 studied the problem of FTS and stabilization of singular fractional-order switched systems without time delays by using multiple Lyapunov functions and LMIs techniques.…”

“…By employing suitable Lyapunov–Krasovskii functional combined with Wirtinger‐based inequality, a set of sufficient conditions ensuring the finite‐time extended dissipative performance for the considered fuzzy systems were presented in terms of LMIs in this work. Later, this concept was developed for FOs and many important results have been addressed for many kinds of FOs by various approaches 19‐28 . By improved fractional‐order Gronwall integral inequality with time delays, Du and Lu have solved the problem for some kinds of fractional‐order neural networks model such as Hopfield neural networks, 19 and bidirectional associative memory neural networks, 20 fuzzy cellular neural networks, 21 and Cohen‐Grossberg memristive neural networks 22 .…”