Reachability Analysis-Based Interval Estimation for Discrete-Time Takagi-Sugeno Fuzzy Systems

Considering disturbances, noise, and sensor faults, this article investigates interval estimation for discrete-time Takagi-Sugeno fuzzy systems. To obtain precise estimation results and attenuate disturbances and noise in the system simultaneously, we integrate robust observers based on the H_{\infty } technique and reachability analysis. Two novel observer gain computation methods are proposed for different purposes. The time-invariant method relaxes the original design conditions by transforming the parameterized linear matrix inequality (LMI) into a series of LMIs to increase computational speed, while the time-varying method employs the parameterized LMI directly and conducts calculation online. Furthermore, reachable set representations for error dynamics are formulated by making use of both time-invariant observer gain and time-varying observer gain. An inverted pendulum system simulation and a comparative numerical simulation are studied to illustrate the effectiveness and superiority of the developed methods.