Lyapunov-Based Switched Control of a Morphing-Wing Tailless UCAV: Formal Stability Guarantees Under Underactuated Switched Nonlinear Dynamics

This paper presents a formally verified and embedded-deployable flight control system for the Sigma-Raven, a morphingwing tailless Unmanned Combat Aerial Vehicle (UCAV) with three discrete wing-sweep configurations, no vertical tail, andstructurally underactuated control surfaces whose input matrix has rank two in a six-dimensional state space. The proposedhybrid control law combines mode-scheduled Linear Quadratic Regulation (LQR) with Higher-Order Sliding Mode (HOSM)super-twisting augmentation for the pitch-unstable low-sweep configuration, governed by an MLF-derived dwell-time constraintof 2.787 s derived analytically as a worst-case energy-dissipation waiting time. Global Uniform Asymptotic Stability (GUAS)is formally proven via the multiple Lyapunov function framework, and yaw stabilisation without a dedicated yaw actuator isestablished via Input-to-State Stability (ISS) exploiting roll-yaw aerodynamic coupling. A two-stage Monte Carlo campaign of500 nominal trials at 20% parametric uncertainty achieves 99.8% success, while an extended campaign of 400 trials under twicethe nominal initial conditions and 40% uncertainty achieves 77.2% at the nominal design point and up to 97.6% under narrowinitial conditions, with failure mode analysis identifying roll saturation, sideslip divergence, and dwell-time boundary cases asthe primary failure mechanisms. The algorithm is translated to portable ISO C (C17, ISO/IEC 9899:2018) via MATLAB CoderR2024b and verified through Software-in-the-Loop (SIL) testing to floating-point precision, with estimated worst-case executiontime below 100 µs at 1 kHz, confirming readiness for deployment on flight-qualified processors.