Impulsive stabilization of delayed neural networks with and without uncertainty

Abstract

SUMMARYMany dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviours due to abrupt jumps at certain instants during the dynamical process, and these complex dynamic behaviours can be modelled by impulsive differential systems. This paper formulates and studies the impulsive stabilization of the Hopfield-type delayed neural networks with and without uncertainty. Several criteria guaranteeing stabilization of such systems are established by employing Lyapunov-like stability theorem, linear matrix inequality approach, and other inequality techniques. A simple approach to the design of an impulsive controller is then presented. Two numerical examples are given for illustration of the theoretical results.

Robust stochastic stability of uncertain discrete-time impulsive Markovian jump delay systems with multiplicative noises

“…For example, when neural networks are used to model human motor tasks involving visual feedback, the effects of state-multiplicative noise, Markovian jumps and time delay should be taken into account (Stoica & Yaesh, 2008), and the impulse effects are also likely to exist in the neural network systems (Li & Liao, 2007;Xu et al, 2010;Zhang & Chen, 2008;Zhu & Cao, 2012). Therefore, the study of Markovian jump delay systems with multiplicative noises and impulses is of practical usefulness in the fields of engineering.…”

“…For this kind of systems, the interested readers are referred to Cao and Lam (1999), Shi et al (1999), Boukas and Liu (2001); Boukas et al (2002), Wang et al (2004); Xiong and Lam (2006); Huang et al (2007); Li and Liao (2007); Lou and Cui (2007), Pan et al (2008), Stoica and Yaesh (2008), Zhang and Chen (2008), Fei, Gao, et al (2009a), Fei, Wang, Gao, and Zhang (2009b), Huang and Mao (2009), Liu and Hill by systems with multiplicative noises, and some characteristics of nonlinear systems can be closely approximated by models with multiplicative noises rather than by linearised models (Wang, Yang, Ho, & Liu, 2007). Many applications of this kind of models can be found in engineering and finance fields, see Gershon, Shaked, and Yaesh (2001), Dragan and Morozan (2002), Wang et al (2007), Stoica and Yaesh (2008), Hou, Zhang, and Ma (2010), Costa and de Oliveira (2012) and the references therein.…”

Hybrid control of stochastic chaotic system based on memristive Lorenz system with discrete and distributed time‐varying delays

“…In many branches of science and industry, the so‐called impulses, which refer to the phenomena that state jumps or resets instantaneously at some discrete times, are usually encountered. Nevertheless, impulses were also used to design controllers to realise the preset goals [24–30]. Impulsive control only requires small control gain and works at some discrete time instants and it can adapt to many fields, thus, it is very attractive.…”

Complete controllability for abstract measure differential systems

“…As well known, abstract measure differential systems are a class of very general systems, which include differential systems, impulsive differential systems, and difference systems as special cases. Work on differential systems, impulsive differential systems and difference systems has contributed greatly to engineering, physics, chemistry, kinematics, communication, and so on . The research on abstract measure differential systems may derive some general view for them all.…”