TS Fuzzy Observer-Based Controller Design for a Class of Discrete-Time Nonlinear Systems

This article presents an observer-based control design approach for a class of nonlinear discrete-time systems. The model nonlinearities are handled in two ways: 1) A Takagi–Sugeno fuzzy representation is used for nonlinearities that depend on measured states, and 2) nonlinearities that depend on unmeasured states are kept in their original form and handled using a slope-bound condition. The observer-based controller design conditions are given as linear matrix inequalities. The approach we propose significantly improves results in the literature by providing less restrictive design conditions. These improvements are illustrated in a detailed analytical and numerical comparison on a synthetic example; while a pendulum-on-a-cart example shows that the approach works both in simulation and in real-time experiments.