Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays

Abstract

This paper is concerned with the global fixed-time synchronization issue for semi-Markovian jumping neural networks with time-varying delays. A novel state-feedback controller, which includes integral terms and time-varying delay terms, is designed to realize the fixed-time synchronization goal between the drive system and the response system. By applying the Lyapunov functional approach and matrix inequality analysis technique, the fixed-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

Fixed‐time synchronization for discontinuous delayed complex‐valued networks with semi‐Markovian switching and hybrid couplings via adaptive control

“…Suppose that Assumptions 1 and 2 hold. Under controller (37) with the adaptive control laws (38) and (39), the controlled network (36) can achieve the global fixed-time synchronization, if there exist Q r > 0, H r > 0, K r > 0,K r > 0 and Δ > 0, and constant * i1 > 0, * i2 > 0, where r ∈ S, such that…”

“…However, unlike Markovian switching systems, the transition rates in semi‐Markovian switching systems are dependent on sojourn‐time and its sojourn‐time obeys nonexponential distributions, such as Gaussian distribution, Laplace distribution, Weibull distribution, and so on. As we know, many research results with respect to synchronization and stability for semi‐Markovian switching RVDNs can be found, for example, see References 35‐41. In Reference 35, the authors considered global synchronization problems for delayed nonlinear systems with semi‐Markovian switching and hybrid couplings by designing a sliding mode controller.…”

Robust Fixed-Time Synchronization for Coupled Delayed Neural Networks with Discontinuous Activations Subject to a Quadratic Polynomial Growth

“…At present, as a kind of efficient control strategies, the fixed-time synchronization control has received tremendous attention from many researchers. e global fixed-time synchronization was discussed for semi-Markovian jumping neural networks with time-varying delays and discontinuous activation functions in [29]. e authors discussed the global fixed-time stability of dynamical nonlinear systems and realized the global fixed-time synchronization for CNNs with discontinuous activations in [30].…”

New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time‐varying delay components and reaction‐diffusion terms

“…It is known to us all, time delays are often inevitable due to internal or external uncertainties in signal transmission. And the produced time delays may cause the stability of the system and even results in oscillation, divergence, and instability phenomena 27‐30 . Thus, much achievement has been devoted to analyze dynamic behaviors of MNNs with various types of time delays (see, eg, References 6 and 31‐35).…”