Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays

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

“…The RISpS property means that state of the closed-loop system (7) will eventually enter the set B(0, γ c (|v| ∞ ) + d c ) bounded by the threshold parameter ξ 2 and the exogenous disturbance |v| ∞ . This dynamical performance is quite different from and more general than the asymptotical stability [6,14], robust stability [16][17][18][19][20][21][22][23][24][25][26][27], and the conventional ISS [10,12,13]. Furthermore, from the point of view of technique analysis, we adopt the Lyapunov function method for the dynamics of state x(t) while the impulsive jumping estimation method for the control input u(t k ) at event-triggering instants, which shows some hybrid characteristics and is quite different from the common L-K functional approach used in [16-18, 21-27, 48].…”

“…That means our result is feasible and computable. In addition, it is readily observed that the linear matrix inequalities (LMIs) (45)-(49) have smaller dimensions and fewer variables than those given in [16][17][18][19][20][21][22][23][24][25][26][27], which leads to a lower computation complexity.…”

“…Hence the uncertain parameters of a system are only due to the deviations and perturbations of its parameters. Recently, significant progress has been made in the study of robust stability and controller synthesis for delayed systems with parameter uncertainties [16][17][18][19][20][21][22][23][24][25][26][27]. For example, in [17], the robust stability has been studied for a class of linear networked control systems with dynamic quantization, variable sampling intervals as well as communication delays.…”

“…(1) The RISpS property is, for the first time, proposed to evaluate the dynamical behaviors for a class of uncertain delayed systems with disturbances, which is quite different from and more comprehensive than the ISS properties investigated in [7-10, 12, 13, 15, 34-36] and the robust stability studied in [16][17][18][19][20][21][22][23][24][25][26][27]. (2) Several previous literature such as [1,3,6,11,23,27] required that the control signal updates continuously with time, which may lead to the unnecessary cost of network resources. In this paper, the event-triggered scheme is introduced to generates a sporadic control sequence while maintaining the desired ISpS dynamical performance for all admissible uncertainties.…”

Asymptotic stability in probability for discrete‐time stochastic coupled systems on networks with multiple dispersal

“…The last decade has seen considerable research on coupled systems on networks (CSNs) due to their extensive applications in physics, 1,2 epidemiology, 3 and neural networks. [4][5][6][7][8][9][10] Although it is well known that stability analysis of CSNs is a prerequisite and essential work, examining the stability of CSNs is generally a challenging task since the connections between stable and isolated units do not guarantee the stability of CSNs and may even introduce instability. Fortunately, Li and Shuai 11 and Guo et al 12 proposed the graph theory combined with the Lyapunov method to explore the global stability of CSNs.…”