This research focuses on exploring the exponential \(H_\infty \) stability of general conformable nonlinear system. In order to address the nonlinearity inherent in the system, a polynomial fuzzy (PF) method is employed. Modeling a general conformable nonlinear system within the polynomial framework reduces the number of fuzzy rules compared to the classical Takagi–Sugeno fuzzy (TSF). Furthermore, controlling such a complex system, which accounts for perturbations, employs a PF model instead TSF model to describe its nonlinear dynamics, and incorporates a general conformable derivative instead of an integer-order one, is significantly more challenging, and remains unaddressed in previous studies. In this paper, a PF controller is designed in the form of sum of squares (SOS) to enhance the resilience against perturbations and ensure the exponential stability of the proposed model. The proposed SOS can be solved numerically, and partially symbolically, using the recently developed SOSTOOLS. In order to ensure the \(H_\infty \) performance, a generalized criterion is defined for the general conformable nonlinear system. To demonstrate the effectiveness of the proposed method, a numerical example is provided.
