On solutions of the Riccati equation in optimization problems
Bernard Friedland · IEEE Transactions on Automatic Control · 1967
The differenceDbetween two solutionsSandMof the matrix Riccati equation.-\dot{M} = MA + A'M + MBM + Cis given byD = RQ^{-1}R', where-\dot{R} = (A+SB)Rand-\dot{Q}= RBR'. These relations can be used to evaluateM(t)fort < Tarising in optimization problems in whichM(T)does not exist. The relations can also be used to compare the solution of the Riccati equation with its asymptotic solution.