Global Stability Ensured Controller Design for Nonlinear Markov Jump Systems Based on Contraction Theory

This paper presents a novel state feedback controller design method based on contraction theory for continuous-time nonlinear Markov jump systems (NMJSs) to achieve the global stability. The developed approach employs the concept of virtual displacement to transform the global stability problem in Riemannian space into a piece wise local analysis. To address the limitations of traditional Lyapunov methods that rely on the initial values of system states and information at equilibrium points, a Lyapunov-like function is constructed in the tangent space of the system’s state space. The constructed function evolves dynamically with variations in both time and state. This allows for stability analysis that does not depend on initial conditions or equilibrium information. As a result, the global stability of NMJSs is guaranteed. Furthermore, a state feedback control methodology is developed to make the designed controller effective on a global scale. The effectiveness and superiority of the proposed method are illustrated through both a numerical example and an application to aircraft.