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Polynomial Description for Nonlinear Time-Varying Systems

In this paper, a structure called as Polynomial Time-Varying Fuzzy Model (PTVFM) for representing nonlinear systems with time-varying parameters is proposed by using polynomial descriptions. The descriptions as Takagi-Sugeno (T-S) fuzzy model, polynomial fuzzy model and Linear Parameter Varying (LPV) model are respectively applied for nonlinearity, polynomial structure and time-varying parameters. Comparing with the existing works, only few fuzzy rules are required by the proposed structure for approximating the nonlinear systems. Based on the proposed model, only few fuzzy rules are required to describe the systems that reduces the difficulty and complexity of stability analysis. Finally, the comparisons between each model are presented for the approximation accuracy with mean squared error.