Mode-dependent delays for dissipative filtering of stochastic semi-Markovian jump for neural networks

Abstract

AbstractThis work is concerned with the issue of dissipative filtering for stochastic semi-Markovian jump via neural networks where the time-varying delay is based upon another semi-Markov process. Dissipative performance analysis is employed to solve a mode-dependent filtering problem in a unified way. To achieve this task, we implemented the recently proposed notion of extended dissipativity, which gives an inequality equivalent to the well-known $H_{\infty }$ H ∞ , $L_{2}$ L 2 –$L_{\infty }$ L ∞ , and dissipative performances. Different from the existing literature (Arslan et al. in Neural Netw 91:11–21, 2017; Chen et al. in ISA Trans. 101:170–176, 2020) where mostly delay-free filters have been investigated, our filter contains a communication delay. Based upon the delay-dependent conditions, for the analysis of stochastic stability and extended dissipativity for neural networks with time-varying delays, our results are obtained by using a mode-dependent Lyapunov–Krasovskii functional together with a novel integral inequality. Original stochastic filtering conditions are characterized by linear matrix inequalities. A numerical simulation is elaborated to elucidate the feasibility of the proposed design methodology.