Generalized matrix sign function algorithm for algebraic riccati equation

Abstract

It is not possible to use effective numerical methods (the matrix sign function method, the Schur method and other (see, for example Aliev and Larin, 1998; Petkov, et.al, 1991) for solving ARE, which Hamiltonian matrix has eigenvalues on the imaginary axis. It is essential, that so-called strong solution (see, Park and Kailath 1996) may be the solution of such type of ARE. In this paper the algorithm of construction of the solution of ARE, which Hamiltonian matrix has eigenvalues on the imaginary axis, are brought. This algorithms can be interpreted as generalized sign function method.