Global stabilisation for Markov jump nonlinear systems based on contraction theory

The paper introduces a contraction theory-based method for designing state-feedback controllers in Markov Jump Nonlinear Systems(MJNSs). Compared to conventional Lyapunov-based approaches, whose stability guarantees typically depend on specific equilibrium points and initial conditions, the proposed method offers a more general and flexible solution. Within a Riemannian manifold framework, a virtual displacement is introduced to construct a function in the tangent space that evolves continuously with time and system states. This evolving function is then utilised to derive the feedback gain that guarantees global controller performance. The proposed method is validated through a numerical study and a maritime navigation application, demonstrating its effectiveness and superiority.