Stability Analysis of TS Systems via Reduced-Complexity Affine Representation

This paper presents a systematic approach to reduce the complexity of sector nonlinearity TS fuzzy models using existing linear dependencies between local linear submodels. The proposed approach results in a decrease of the fuzzy model rules from 2p to p + 1 rules while maintaining equivalence to the TS fuzzy model. An LMI formulation is presented to obtain conditions for stability analysis with an example to offer a comparison between the two models. The main purpose of reduced-complexity models is to keep the design and the structure of the nonlinear control and observer schemes as simple as possible for real-time implementation, especially when dealing with highly nonlinear systems with a very large number of premise variables. A real-world robotic example is provided to highlight the interests and current limitations of the proposed approach.