Hybrid gain-scheduled PI control with a closed-form contraction compensator for longitudinal stabilisation of...

Morphing-wing unmanned aerial vehicles reshape their wings in flight to reconcile conflicting mission profiles. This reshaping induces large, rapid variations in inertia and aerodynamic coefficients that make longitudinal stabilisation difficult. Conventional linear parameter varying gain-scheduled controllers bound the input/output gain but do not quantify the steady-state tracking error under unmodelled perturbations and actuator saturation. We close this gap with a hybrid controller of two parts. An Enhanced Structural Proportional-Integral baseline that augments the gain-scheduled law with back-calculation anti-windup, adaptive integral action, morphing-rate feedforward, and pitch-speed cross-coupling; and a physics-structured dynamic compensator built on a closed-form continuous-time recurrence whose weights are fixed by a sign-constrained design rather than trained on data, keeping the compensator interpretable and its stability certificate exact. We prove a parameter-dependent Lyapunov inequality with a rate-bounded derivative that yields a closed-form ultimate bound on the tracking error, certified first on a scheduling grid and then strengthened to a strictly global certificate over the scheduling polytope through a vertex semidefinite feasibility problem. The compensator carries a closed-form contraction certificate together with an input-to-state stability bound. In Monte-Carlo experiments with [Formula: see text] aerodynamic uncertainty, the controller reduces root mean square pitch error by over [Formula: see text], overshoot by over [Formula: see text], settling time by over [Formula: see text], and throttle total variation by over [Formula: see text] relative to the historical baseline, at a per-step computational cost compatible with embedded execution.