A Fully Actuated System Approach to Interval Observer Design with Applications in Fault Detection

This paper explores a fully actuated system approach for interval observer design with applications in fault detection. Leveraging the full-actuation property, a stabilization control law is initially implemented to cancel open-loop nonlinearities, resulting in a constant high-order linear system. Subsequently, two interval observer design approaches are introduced. Employing the parametric design method, the challenge of determining the observer gain and nonsingular transformation matrix is converted into solving the generalized Sylvester matrix equation. This method allows for the free assignment of the eigenstructure of the observer error system. Additionally, a fault detection logic is presented. Finally, the feasibility and effectiveness of the proposed interval observers are demonstrated through an illustrative example.