Mittag-Leffler stability of impulsive fractional-order bi-directional associative memory neural networks with time-varying delays

Abstract

In the paper, a class of impulsive Caputo fractional-order bi-directional associative memory neural networks with time-varying delays is considered. Applying the fractional Lyapunov method, a sufficient condition for Mittag-Leffler stability of the equilibrium point of the system under consideration is derived. Some earlier results are extended and improved. Our results provide an impulsive control law which stabilizes the impulse-free fractional-order neural network time-delay model. An example is provided to demonstrate the effectiveness of the proposed results.

Event-based robust stabilization for delayed systems with parameter uncertainties and exogenous disturbances

“…then the closed-loop system (7) is robustly input-to-state practically stable with respect to all parameter uncertainties satisfying (2).…”

“…When all uncertainties are removed, Definition 1 reduces to the conventional ISS concept introduced in [11,12,34] and the term γ c (|v| ∞ ) + d c is used to represent the bound of the domain where the state remains. When d c = 0 and v(t) ≡ 0, Definition 1 reduces to the asymptotically robust stability considered in [20][21][22][24][25][26] and the KL-function β c indicates that the state will tend to zero as t → +∞ for all admissible parameter uncertainties satisfying (2).…”

“…As is well known, the time delays can influence the dynamic of systems seriously and may cause some unstable performances such as divergence, oscillation or chaotic. Over the past few years, a great number of research papers have been published to focus on the stability and stabilization of dynamical systems with time delays (see [1][2][3][4][5][6] and the references cited therein). At the same time, it should be mentioned that under some exogenous disturbances, the system states may evolve in a bounded domain rather than converge to an equilibrium point, which indicates that the conventional stability cannot be realized.…”

A fractional super-twisting control of electrically driven mechanical systems

“…Nevertheless, this type of STA requires the integer-order differentiability of unknown inputs. In contrast, fractional-order operators have been developed recently for controlling complex dynamics (Efe, 2011; Muñoz-Vázquez et al, 2018a,b; Stamova et al, 2017), exploiting the advance and diverse memory effects inherent to these class of operators (Martínez-Fuentes and Martínez-Guerra, 2018, 2019). For instance, sliding mode controllers with fractional dynamic references have been proposed (Fei and Lu, 2018; Wang et al,.…”

Non-smooth convex Lyapunov functions for stability analysis of fractional-order systems

“…Fractional calculus foundation is as old as the conventional integer-order calculus (Podlubny, 1999); moreover, despite there having been reported recent impressive advances in theory and applications (Chen K et al, 2017; Efe, 2011; Stamova et al, 2017), there remains some fundamental open problems in modelling, control and stability analysis for fractional-order nonlinear systems. The importance of fractional calculus becomes evident when studying some characteristics of advanced physical phenomena, which are better and more deeply understood by considering inherent features of fractional operators, such as non-locality, memory and heritage.…”