Performance of Lyapunov Solvers on Dedicated SLICOT Benchmarks Collections

Abstract

Lyapunov equations are often encountered in control theory and its applications, including system balancing, model and controller order reduction, and stability analyses. An accuracy-enhancing solver for standard and generalized continuous- and discretetime Lyapunov equations is investigated in this paper. It has been derived by specializing a solver for algebraic Riccati equations based on Newton's method. The conceptual algorithm and some implementation details are summarized. The numerical results obtained by solving sets of examples of increasing dimension and numerical difficulty from the SLICOT benchmark collections for Lyapunov equations are analyzed and compared to the solutions computed by the state-of-the-art MATLAB and SLICOT solvers. The results show that most often the new solver is more accurate, sometimes by several orders of magnitude, than its competitors, and requires only a small increase of the computational effort.