An innovative approach to designing unknown-input observers in Takagi–Sugeno systems

The main objective of this research is to introduce an innovative and advanced methodology for the design of unknown-input observers adapted to continuous-time Takagi–Sugeno (T–S) systems. We focus on the development of functional observers capable of handling the unknown inputs present in the state and output equations. The design and analysis of these observers are strongly based on the principles of Lyapunov–Krasovskiĭ stability theory, providing a robust and theoretically powerful background. The convergence criteria for these observers are structured according to the formulation of linear matrix inequalities, providing a strict basis for stability analysis. In order to underline the effectiveness of the proposed approach, we offer full validation through simulation results derived from two numerical examples. These examples serve as specific demonstrations of the performance of the designed observers, highlighting their effectiveness in both reduced-order and full-order scenarios. Through this detailed exploration, we aim to highlight the applicability in actual applications and the reliability of our methodology introduced in the field of unknown-input observers for T–S systems.