Polar coordinate fuzzy model and stability analysis

This paper presents a polar coordinate fuzzy model and its stability condition. The new polar coordinate fuzzy model can exactly represent a class of nonlinear systems globally or semi-globally. The polar coordinate fuzzy model has local linear parameter varying models which are linear with respect to distance r in the polar coordinate. The varying parameters consist of sum and/or products of sin and/or cos with respect to angles θ₁, θ₂, ..., θ_n-1 in the polar coordinate. The distance and angles can be calculated from state variables. Furthermore, we derive a stability condition for a polar coordinate fuzzy model. An example illustrates the utility of this approach.