Adaptive Control of Discrete-Time State-Space T-S Fuzzy Systems

This paper develops a new solution framework for adaptive control of general discrete-time state-space T-S fuzzy systems with a relative degree rho (1 <= rho <= n). A new procedure is proposed to construct a global T-S fuzzy system model from local state-space models in non-canonical form, which has an explicit relative degree structure and a specific input-output signal causality relationship in the sense that it does not include any future values of fuzzy membership functions. An adaptive feedback control scheme is designed based on the global T-S fuzzy model, to ensure desired stability and tracking. As an illustrative example, a T-S fuzzy system is constructed based on the linearized local models of a transport airplane. Simulation results have demonstrated the developed new concepts and verified the desired performance of the new type of adaptive fuzzy control systems.