A data-driven online stability monitoring method for unknown discrete-time nonlinear systems

This paper proposes a data-driven stability criterion based on the geometric interpretation of quadratic Lyapunov functions, which can be used for online stability assessment of unknown discrete-time nonlinear systems. The paper shows that the existence of a Quadratic Lyapunov Function can only be guaranteed if the intersection of the positive real space and the convex cone determined by the data set transformed from the measured states with a suitable orthogonal matrix is not empty, which can be numerically determined by solving a max-min problem. The stability judgment can be given according to the sign of the optimized value. The proposed method requires no system model but only the measurements of system states. Numerical examples are given to show the effectiveness of the proposed method.