Finite-Time $\mathcal {L}_{2}$-$\mathcal {L}_{\infty }$ Synchronization for Semi-Markov Jump Inertial Neural Networks Using Sampled Data

Abstract

This paper investigates the finite-time synchronization issue for semi-Markov jump inertial neural networks, in which the sampled-data control is employed to alleviate the burden of the limited communication bandwidth. Due to the existence of inertial item, the semi-Markov jump inertial neural networks as hybrid neural systems, are depicted with secondorder derivatives for the first time, which can be turned to firstorder derivatives by the variable transformation. Furthermore, by applying appropriate integral inequalities and constructing the proper Lyapunov functional, some sufficient conditions, which not only guarantee the finite-time synchronization of the resulting error system but also ensure a specified level of L2-L∞ performance, are acquired based on the optimization of integral inequality technique. A numerical example is, eventually, proposed to substantiate the validity of the developed method.

Finite-Time H State Estimation for PDT-Switched Genetic Regulatory Networks With Randomly Occurring Uncertainties

“…Definition 2: [44] For 0 ≤ a 1 < a 2 and R > 0, EES is stochastically finite-time stable (SFTS) with respect to (a 1 , a 2 , R, N ) when the disturbance is zero, for ∀t ∈…”

H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information

“…In this subsection, based on Theorem 1, a mode-dependent controller is constructed by utilizing the CCL algorithm. N (a = b), and = 1, 2, the relations (19), (21), (22) and the following inequality hold:…”

“…This completes the proof. ∀a, b ∈ N (a = b), and = 1, 2, the relations (19), (21) and the following conditions hold:…”

“…Detailedly, the critical process of the CCL algorithm is to transfer the solving of condition (19), (21) and (33)- (35) into verifying the feasibility of (37) subject to (19), (21), (33), (34), (38) and (39). If they are feasible, the matrices Q aτ , P a (τ ),K a should be calculated.…”

“…If they are feasible, the matrices Q aτ , P a (τ ),K a should be calculated. Moreover, we have to substitute these solved matrices into condition (19), (21), (22) and (31) to determine whether they are feasibility. Only when these condition are feasible, the expected controller gain can be calculated by (36).…”