LAUSR

This article presents the results on delay-dependent conditions of extended quantized T–S fuzzy filtering based on Markovian switch system (Q-FMSS) in the existence of communication delays via a channel. Different from the existing fuzzy filter, a new fuzzy filter is proposed to receive not only the quantized output of the system but also gets the quantized delay output. The purpose of this paper is to solve the $$H_{\infty }$$H∞, $$L_{2}$$L2 -$$L_{\infty }$$L∞, passive and dissipative filtering problems. The extended dissipative inequality contains several weighting matrices. By tuning the weighting matrices, the extended dissipativity will reduce to the $$H_{\infty }$$H∞ performance, $$L_{2}$$L2 -$$L_{\infty }$$L∞ performance, passivity and dissipativity, respectively. Another drive of this paper is to fully investigate the properties of Transition Rates (TRs) of Markovian switch system with Membership Function (MF) by implementing the novel fuzzy Markovian Lyapunov–Krasovskii functional to obtain the sufficient LMI conditions (delay dependent) for stochastically stability and performance analysis of resulting error system. Extended dissipativity notation is employed to resolve the resulting error system to consider the $$H_{\infty }$$H∞, $$L_{2}-L_{\infty }$$L2-L∞, dissipativity and passivity analyses, which are important for the power systems. Finally, a tunnel-diode example is given to elaborate the potentiality and effectiveness of the proposed design technique.