Singular perturbation of an infinite interval linear state regulator problem in optimal control

AbstractThe corresponding problem on a finite interval has been studied by O'Malley and Kung using two different methods, namely: (1) the two-point boundary value method (O'Malley and Kung, SIAM J. Control 13 (1975), 327–337) and (2) The Riccati gain method (O'Malley and Kung, J. Differential Eqs. 16 (1974), 413–427). For the infinite interval, the two-point boundary value method is no longer relevant. However, the Riccati gain method can be applied. The conditions are changed slightly from those for the finite interval case. Some conditions are eliminated and some new conditions are added