  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 a trust-region
method.
  Numerical experiments illustrate that for large-scale problems the
trust-region method is more effective than the steepest descent and the
conjugate gradient methods. 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.
