Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities

Saravanan Shanmugam , R Vadivel , Mohamed Rhaima , Hamza Ghoudi (1)

1 MODAL'X - Modélisation aléatoire de Paris X

The issue of extended dissipative analysis for neural networks (NNs) with additive time-varying delays (ATVDs) is examined in this research. Some less conservative sufficient conditions are obtained to ensure the NNs are asymptotically stable and extended dissipative by building the agumented Lyapunov-Krasovskii functional, which is achieved by utilizing some mathematical techniques with improved integral inequalities like auxiliary function-based integral inequalities (gives a tighter upper bound). The present study aims to solve the H ∞ , L 2-L ∞ , passivity and (Q, S , R)-γ-dissipativity performance in a unified framework based on the extended dissipativity concept. Following this, the condition for the solvability of the designed NNs with ATVDs is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach were demonstrated through four numerical examples.

Mots clés: neural networks linear matrix inequality extended dissipative additive time-varying delay Lyapunov-Krasovskii functional Mathematics Subject Classification: 93D20; 92B20; neural networks; linear matrix inequality; extended dissipative; additive time-varying delay; Lyapunov-Krasovskii functional Mathematics Subject Classification: 93D20

Domaines: Mathématiques [math]

Saravanan Shanmugam, R Vadivel, Mohamed Rhaima, Hamza Ghoudi. Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities. AIMS Mathematics, 2023, 8, pp.21221 - 21245. ⟨10.3934/math.20231082⟩. ⟨hal-04445400⟩