Generalized extended state observer‐based control for polynomial parameter‐varying systems with mismatched uncertainties

Abstract This paper investigates the closed‐loop stability of generalized extended state observer‐based control (GESOBC) for polynomial parameter‐varying (PPV) systems with mismatched uncertainties under partially/completely unmeasurable states. A novel generalized extended state observer (GESO) is introduced, and new input‐to‐state stability (ISS) conditions for the closed‐loop system are derived‐based Lyapunov theory, expressed as state‐and‐parameter‐dependent matrix inequalities. Particularly, by constructing augmented vectors and applying a key lemma, the proposed method eliminates bilinear terms involving products of controller gain matrices with Lyapunov functions, as well as cross‐coupling terms between measurable and unmeasurable states. In addition, the resulting solvable conditions can be efficiently solved using sum‐of‐squares (SOS) convex optimization techniques. Notably, the developed framework neither requires the plant to satisfy standard integral‐chain structure nor demands uncertainty matching conditions. Furthermore, the separation principle holds between the controller and observer designs. Finally, two numerical examples validate the method's feasibility and effectiveness.