Homographic scheme for Riccati equation
It provides a stable numerical method for a known equation in control theory, but the contribution is incremental as it focuses on a specific numerical scheme without broad impact.
The paper presents a numerical scheme for solving the matrix Riccati equation in control problems, proving convergence in the scalar case and demonstrating unconditional stability and positive definiteness through numerical experiments.
In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.