Numerical solution of large Lyapunov equations

摘要: A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix considered. For single input case, i.e., when equation considered of form AX + XA(sup T) bb(sup = 0, b column vector, existence approximate solutions X VGV(sup V N x m and G m, with established. first class based on use numerical quadrature formulas, such as Gauss-Laguerre applied to controllability Grammian. second projection process Galerkin type. Numerical experiments presented test effectiveness these