Adaptive control of discrete-time state-space T–S fuzzy systems with general relative degree

This paper develops a new solution framework for adaptive control of general discrete-time single-input single-output (SISO) state-space Takagi–Sugeno (T–S) fuzzy systems with a relative degree ρ ( 1 ≤ ρ ≤ n ). A new procedure is proposed to construct a normal form of a global T–S fuzzy system model from local state-space models in non-canonical form, and such a normal form system 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 normal form T–S fuzzy model, to ensure desired closed-loop stability and output tracking properties. A comparison is given to adaptive state tracking designs seen in the literature, which require much more restrictive matching conditions and do not take into account the high relative degree cases. 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.