Exponential Lagrange stability for impulses in discrete-time delayed recurrent neural networks

Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

“…Furthermore, since α, β, L 1 i and L 2 i are known and other parameters can be computed in terms of Remark 3, i ∈ N. us, the bound of k can be calculated easily by (32). Additionally, we select the appropriate k and substitute it into transcendental equation (18) with other parameters together so that the length of the argument interval can be acquired. Finally, a comprehensive selection of values that satisfy both k and θ inequality conditions in eorem 1 can ensure the exponential stability of NPRNN (7).…”

“…Investigation and synthesis of recurrent neural networks (RNNs) is an unfailing subject regardless of past and present due to its wide application in image and object recognition, speech recognition, model prediction, automatic control, signal processing, and so forth [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Various stability types for RNNs have been proposed and deeply explored, for instance, asymptotic stability [1][2][3], exponential stability [4][5][6], and multistability [7,8].…”

“…Various stability types for RNNs have been proposed and deeply explored, for instance, asymptotic stability [1][2][3], exponential stability [4][5][6], and multistability [7,8]. Moreover, some other stability types have been further developed in recent five years, such as synchronization [9,10], impulsive stochastic stability [11], region stability [12], global Mittag-Leffler stabilization [13,14], memristor-based dynamic behavior stability [15,16], antiperiodic stability [17], exponential Lagrange stability [18] and so on. In fact, compared with the general stability, the study of global exponential stability can be convenient for us to know the convergence rate of the system within a fast time interval accurately and intuitively.…”

Further Results on Exponentially Robust Stability of Uncertain Connection Weights of Neutral-Type Recurrent Neural Networks

“…Accordingly, with the in-depth study of RNNs, it can be seen that the stability is a forerunner condition for the multifarious practical applications. Hence, the research on the stability of the system is becoming more and more abundant [1][2][3][4][5][6][7][8][9][10][11][12][13][14], such as asymptotic stability [1], exponential stability [2][3][4], multistability [5], synchronization [6], dissipativity [3,7,8], region stability [9], memristorbased dynamic behavior stability [10], and exponential Lagrange stability [11,12]. Additionally, in terms of the widespread application fields such as the visual optimization, image processing, language recognition, associative memory, and other fields, the stability of RNNs has become an indispensable dynamical behavior characteristic which must be further considered.…”