Abstract
This paper is mainly concerned with improved stability criteria for generalized neural networks (GNNs) with time-varying delay by delay-partitioning approach. A newly augmented Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed by decomposing integral interval, in which the relationships between the augmented state vectors are fully taken into account. The tighter bounding inequalities such as a Wirtinger-based integral inequality, Peng-Park’s integral inequality, and an auxiliary function-based integral inequality are employed to effectively handle the cross-product terms occurred in derivative of the LKF. As a result, less conservative delay-dependent stability criterion can be achieved in terms of $e_{s}$ and LMIs. Finally, two numerical examples are included to show that the proposed results are less conservative than existing ones.
Highlights
1 Introduction The generalized neural networks (GNNs) model, which is a combination of local field neural networks (LFNNs) and static neural networks (SNNs), has received increasing attention in recent years, due to the fact that it provides an unified frame for stability analysis of both SNNs and LFNNs [ – ]
It should be mentioned that back-propagation neural networks and optimization type neural networks can be modeled as SNNs, whereas Hopfield neural networks, bidirectional associative memory neural networks, and cellular neural networks can be modeled as LFNNs [ ]
When revisiting the aforementioned literature, we find that these works still leave plenty of room for improvement because (a) the constructed Lyapunov-Krasovskii functional (LKF) do not contain adequate delay-partitioning augmented terms and (b) overbounding techniques are applied to estimate the derivatives of the LKFs, which are the origin of conservatism
Summary
The generalized neural networks (GNNs) model, which is a combination of local field neural networks (LFNNs) and static neural networks (SNNs), has received increasing attention in recent years, due to the fact that it provides an unified frame for stability analysis of both SNNs and LFNNs [ – ]. Based on constructing a LKF including more information on activation functions and delay upper bounds, [ ] has derived less conservative stability criteria for GNNs with two time-varying delay components. By proposing an improved integral inequality to handle the cross-product terms occurred in the derivative of the LKF, [ ] has achieved less conservative stability criteria for GNNs with interval time-varying delays via delay bi-partitioning method. By introducing an augmented LKF including triple and four integral terms, [ ] has derived an improved delay-dependent stability criterion for GNNs with additive time-varying delays by the reciprocal convex combination technique. Motivated by the above-mentioned discussion, the main objective of this paper is to develop less conservative stability criteria for GNNs with time-varying delay via tighter bounding inequalities and delay-partitioning approach. (iii) ∃Y ∈ Rn×m: + He{YB} < , where B⊥ ∈ Rn×(n–rank(B)) is the right orthogonal complement of B
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