Abstract
This paper studies the problem of extended dissipativity analysis for Markovian jump neural networks (MJNNs) with time-varying delay. Combining Wirtinger-based double integral inequality and S-procedure lemma, a novel double integral-based delay-product-type (DIDPT) Lyapunov functional is constructed in this paper, which avoids the incomplete components in the existing works. Then, based on parameter-dependent reciprocally convex inequality (PDRCI) and the novel DIDPT, a new extended dissipativity condition is obtained for MJNNs. A numerical example is employed to illustrate the advantages of the proposed method.
Highlights
From the modeling of the biological brain, the concept of neural networks (NNs) is proposed, which have been successfully used in various areas, such as signal processing, associative memories, and pattern recognition [1]–[8]
It is a meaningful topic for the dynamic performance analysis for NNs with time delay [21]–[23]
Definition 1: [24], [25] For prescribed matrices 1, 2, 3, and 4 satisfying Assumption 1, Markovian jump neural networks (MJNNs) (1) are said to be extended dissipative, if there exists a scalar such that the following inequality holds for all nonzero w(t) ∈ L2[0, +∞) and any T ≥ t
Summary
From the modeling of the biological brain, the concept of neural networks (NNs) is proposed, which have been successfully used in various areas, such as signal processing, associative memories, and pattern recognition [1]–[8]. Based on PDRCI and the novel DIDPT functional, a new condition is proposed to ensure MJNNs to be stochastically stable and extended dissipative.
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