Numerical solution of Lyapunov equations related to Markov jump linear systems
Tobias Damm, Kazuhiro Sato, Axel Vierling · Numerical Linear Algebra with Applications · 2017
Summary We suggest and compare different methods for the numerical solution of Lyapunov‐like equations with application to control of Markovian jump linear systems. First, we consider fixed‐point iterations and associated Krylov subspace formulations. Second, we reformulate the equation as an optimization problem and consider steepest descent, conjugate gradient, and trust‐region methods. Numerical experiments illustrate that, for large‐scale problems, the trust‐region method is more efficient than a direct solution or a standard solver for linear matrix inequalities. The fixed‐point approach, however, is superior to the optimization methods. As an application, we consider a networked control system, where the Markov jumps are induced by the wireless communication protocol.