<i>H</i> _∞ Delayed Filtering of Markov Jump Fuzzy Systems in Consumer Electronics: Input–Output Analysis

This article investigates the design of robust H∞ filters for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays, with a critical challenge in many consumer electronics applications. We extend existing research by incorporating Markovian jump parameters to model system uncertainties and considering internal–like time–varying delays, which are prevalent in real-world scenarios such as wireless communication and networked control systems in consumer devices. To address the complexities introduced by time-varying delays, we employ a three-term approximation model that more accurately captures the system dynamics compared to traditional approaches. Furthermore, we incorporate the time derivative of the membership functions (MFs) into the filter design, and its impact on system stability and performance. To ensure filter stability, we derive novel stability conditions based on the mode–dependent Lyapunov-Krasovskii functional approach, incorporating constraints on the higher bounds of the MF time derivatives. Leveraging the small–gain theorem with scaling techniques, we propose the design of both full-order and reduced-order H∞ filters, expressed in terms of linear matrix inequalities (LMIs). These LMI–based solutions provide a systematic and computationally efficient approach for filter synthesis. Finally, we validate the effectiveness of our proposed filtering strategies through illustrative examples drawn from relevant consumer electronics applications, such as noise cancellation in audio devices, image stabilization in cameras, and vibration suppression in wearable devices. The results demonstrate the enhanced robustness and performance of the proposed filters in the presence of time-varying delays and uncertainties.