Global robust stability for delayed neural networks with polytopic type uncertainties

Global robust point dissipativity of interval neural networks with mixed time-varying delays

“…Criteria for the global robust stability of interval neural networks with delay have been presented in [15,16]. The authors established a global robust stability criterion for delayed neural networks with polytopic type uncertainties in [17] and others investigated the global asymptotic robust stability of static neural network models with S-type distributed delays on a finite interval in [18].…”

“…To analyze uncertainty of neural networks, one reasonable method is to assume the parameters in certain intervals. Recently, much attention has been paid to the robust questions of interval neural networks [12][13][14][15][16][17][18]. In [12][13][14], global asymptotic stability and global robust stability of neural networks with time delays have been studied and several sufficient conditions have been derived for the existence and uniqueness of equilibria for interval neural networks with time delays.…”

“…Many appropriate applications are found in some domains such as stability theory, synchronization and control, signal processing, and associative memory. Hence, a great many of results of neural networks have been obtained and most of them are relevant to the stability of neural networks (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). For example, a sufficient condition has been given for cellular neural networks with delay to be completely stable in [1].…”

Relaxed delay-dependent exponential stability condition for a class of neural networks with polytopic uncertainties and distributed delays

“…About the problem of robust stability for the delayed neural networks with polytopic type uncertainties, the parameter-dependent idea in [7] is realized by using Leibniz-Newton formula to introduce some free-weighting matrices; however, in the above-mentioned treatment, some of the free-weighting matrices are still fixed for different vertices of the polytope, which inevitably results in the conservatism of the proposed method. By utilizing parameterdependent Lyapunov functionals and the relaxed linear matrix inequality approach introduced in [9], new sufficient robust global exponential stability conditions were proposed in [8], in which no matrix variables need be fixed for different vertices of the polytope.…”

Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations

“…There are various types of uncertainties under discussion, such as time varying structured uncertainty(see for example, Shamma (1994), Mao et al (1998), Moon et al (2001), Lu et al (2003), Chen et al (2005), Yue and Han (2005), Huang and Mao (2009), Wang and Bai (2012), Kuang and Deng (2012), Hartung et al (2013), Zhu et al (2014a)), polytopic-type uncertainty (Peaucelle et al (2000), Shaked (2001), Xia and Jia (2002), He et al (2005), Li et al (2008), Li et al (2009)), and interval uncertainty (Mao and Selfridge (2001), Mao (2002), Mao and Yuan (2006), Udom (2012)). Robust stability of a uncertain system means that the system will be always stable for any possible quantities of uncertainties.…”