A Novel LMI-Based Design of Rational Control Laws for a Class of Nonlinear Systems Modeled as Differential Algebraic Equations

This letter addresses the problem of controller design for the stabilization of nonlinear systems described by index-1 differential-algebraic equations. A novel synthesis method is proposed in which rational nonlinear control laws are constructed based on a structure known as parallel distributed compensation. The individual components of this structure are determined using convex optimization techniques, specifically through the formulation and solution of conditions expressed as linear matrix inequalities. The proposed approach is validated through a pair of mechanical system examples, both unconstrained and constrained configurations, demonstrating its effectiveness in achieving efficient and robust stabilization of nonlinear differential-algebraic systems.