Stabilization of Nonlinear Systems via Subset-Based Membership Functions and Exact Polytopic Representation

This letter introduces a novel approach for ensuring the asymptotic stabilization of nonlinear systems by constructing an exact polytopic representation of the system in a region of interest using a trapezoidal partition. Unlike traditional methods, such as gain scheduling or piecewise approximations, the proposed approach does not rely on such approximations and ensures that the derived stabilization conditions are directly applicable to the original nonlinear system. A systematic iterative design algorithm is introduced to compute the control gains, guaranteeing asymptotic stabilization for the nonlinear system. The effectiveness of the proposed approach is demonstrated through numerical examples, highlighting its advantages over traditional methods.