Extended Hamiltonian algorithm for the solution of discrete algebraic Lyapunov equations

In this paper, we use a second-order learning algorithm for solving the numerical solution of the discrete algebraic Lyapunov equation. Specifically, Extended Hamiltonian algorithm based on the manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient algorithm, the Riemannian gradient algorithm and the two traditional iteration methods. Simulation examples show that the convergence speed of the Extended Hamiltonian algorithm is the fastest one among these algorithms.