THE RELATIONSHIP BETWEEN THE STABILITY AND THE OPTIMALITY OF LINEAR SYSTEMS(Ⅱ)

Different from the inverse problem put forward by R.E.Kalman, another kind ofinverse problem of linear optimal control is proposed and discussed in1] as follows:Givenan asymptotically stable linear constant system and a nonnegative quadratic performanceindex, when can a state-feedback be separated from the stable system so that this state-feedback control law is optimal for the given index? In this paper this problem is extended.Similar conclusions are obtained for linear discrete systems and linear time-variablesystems. According to these conclusions we can say that the correspondence between theasymptotically stable system and the optimal feedback system is the inherent character ofall kinds of linear systems.