Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and α-inverse Hölder activation functions

Abstract

This paper concerns the problem of enhanced results on robust finite time passivity for uncertain discrete time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov–Krasovskii functional candidate, reciprocally convex combination method, and linear matrix inequality technique, we derive several sufficient conditions for varying the passivity of discrete time BAM neural networks. Further, some sufficient conditions for finite time boundedness and passivity for uncertainties are proposed by employing zero inequalities. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

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].…”

“…When all uncertainties are removed, Definition 1 reduces to the conventional ISS concept introduced in [11,12,34] and the term γ c (|v| ∞ ) + d c is used to represent the bound of the domain where the state remains. When d c = 0 and v(t) ≡ 0, Definition 1 reduces to the asymptotically robust stability considered in [20][21][22][24][25][26] and the KL-function β c indicates that the state will tend to zero as t → +∞ for all admissible parameter uncertainties satisfying (2).…”

“…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.…”