Practical Stabilization of Uncertain Fuzzy Systems: Design Methods and Case Studies in Environmental Control

Abstract

This study develops a feedback stabilization framework for uncertain Takagi–Sugeno (T–S) fuzzy systems, guaranteeing practical exponential stability. A primary contribution is the derivation of sufficient conditions established via Lyapunov analysis, which ensure that all system trajectories converge exponentially to a bounded compact set despite modeling uncertainties, actuator variations, and external perturbations. Compared to existing T–S fuzzy control approaches, our method provides an explicit characterization of the convergence rate and the ultimate bound in terms of perturbation bounds, and handles both matched and unmatched uncertainties simultaneously. The theoretical framework is directly applied to the stabilization of an HVAC (Heating, Ventilation, and Air Conditioning) system for smart building climate control. This application demonstrates the method's effectiveness in maintaining precise temperature and humidity regulation under realistic disturbances, such as occupancy changes and equipment efficiency drift. A detailed numerical example with all matrices explicitly provided and a comprehensive HVAC case study with complete simulation parameters confirm the approach's practical utility for designing resilient, energy efficient control systems in intelligent buildings.