Global Stability Ensured Controller Design for Nonlinear Markov Jump Systems and Application to Aircraft Systems

This study proposes a novel contraction theory-based state feedback controller design framework for continuous-time nonlinear Markov jump systems (NMJSs), with a particular focus on its application to aircraft dynamic control. Given the complex and mode-switching behavior of flight systems under uncertain environments, the method leverages the concept of virtual displacement to convert the global stability analysis in Riemannian space into tractable local evaluations within each mode. Unlike conventional Lyapunov-based approaches that typically depend on known equilibria or specific initial states, this method constructs a Lyapunov-like function within the tangent space of the system. This function dynamically evolves with both time and state, enabling robust stability guarantees that are independent of initial conditions or fixed operating points. A globally effective state feedback control law is subsequently developed, ensuring stability across all system modes. The proposed strategy is validated through a detailed numerical example and further demonstrated in a practical flight control scenario, highlighting its capability to handle uncertainties and mode transitions in aerospace systems more effectively than traditional methods.