Extended dissipative filter design for interval type 2 fuzzy discrete time switched systems with time varying delays

The article examines the topic of extended dissipative filtering design for a class of discrete-time interval type 2 fuzzy switching systems (IT2FSS). The asymptotic stability problem of IT2FSS is handled by employing an average dwell time (ADT) technique that dwells between the subsystems. The IT2FSS under discussion is represented with a time-varying delay, which enables a more precise depiction of nonlinear dynamical systems than conventional state space representation. In comparison to earlier findings, a set of piecewise Lyapunov-Krasovskii functional (LKF) candidates are provided, which are fuzzy and delay-dependent functional. The Lyapunov stability theory-based suitable criterion is derived by the LKF candidates for the stability and performance evaluations of the filtering error system. Extended dissipative filtering is a technique which employs an extended performance index to analyse \( H_{ \infty },\ L_{2} - L_{\infty }, \) $H_{\infty },L_2-L_{\infty },$ passive, and \( (Q, S, R)-\gamma \) $(Q,S,R)-\gamma$ dissipative filtering in a single structure. As a special case, the criteria for constant delay are also discussed. Two real-world numerical examples for both time-varying delay and constant delay demonstrate the applicability and reliability of the known theoretical findings.