Stability of the procedure of explicit recovery of skew-selfadjoint Dirac systems from rational Weyl matrix functions

Abstract

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