Scalar projective synchronization for uncertain T-S fuzzy systems with unified control fluctuation: Implementation to quadruple-tank process model

Abstract

This work intends to the study of the energy-based performances of the Takagi-Sugeno (T-S) fuzzy systems in the presence of parameter uncertainties and non-linear function. This type of fuzzy system refers to an extension of the T-S fuzzy systems, where non-linear terms are directly incorporated into the outcome of the fuzzy rules. The major motive of this study is to examine the scalar projective synchronization criterion of robust master and slave systems via unified control fluctuation, specifically, non-fragility control. In contrast to the current literature, both norm-bounded additive and multiplicative uncertainties are considered in the non-fragile robust state-feedback controller. The sufficient conditions for robust extended dissipative performance of the T-S fuzzy system are derived by utilizing a projective synchronization approach under state feedback controllers with non-fragility and by linearizing the integral terms obtained from the augmented Lyapunov-Krasovskii functional. Finally, numerical examples counting with fuzzified quadruple-tank process system model have been conducted through MATLAB software to demonstrate the importance and efficacy of the given theoretical results.