Skew-selfadjoint Dirac systems: stability of the procedure of explicit solving the inverse problem

A procedure to recover explicitly skew-selfadjoint matrix Dirac systems on semi-axis from rational Weyl functions is considered. Its stability is proved. Some new facts on pseudo-exponential potentials (i.e. explicit solutions of inverse problems)are proved as well. GBDT version of Baecklund-Darboux transformation, methods from system theory and results on algebraic Riccati equations are used for this purpose.