Unified Solutions to Optimal Fuzzy Observer-Based Fault Detection for Discrete-Time Nonlinear Systems

This article is concerned with the optimal fault detection issues for discrete-time nonlinear systems with the aid of Takagi–Sugeno fuzzy dynamic modeling technique. To this end, in the first part of this article, the nonlinear system is formulated in the time-varying fuzzy manner, and based on it, a unified fault detection approach is developed by solving a multiobjective optimization problem. In this sense, the optimal tradeoff between fault detectability and robustness against unknown inputs is ensured by solving the Riccati equation. Meanwhile, a fuzzy fault detection approach is studied in the second part of this article based on piecewise-fuzzy Lyapunov functions, which is realized by solving linear matrix inequalities. Two examples are given at the end of this article to demonstrate the proposed approaches.