Insensitivity of the optimal linear discrete-time regulator xk+1 = Axk+ Buk with quadratic performance index is investigated. Expressions are derived for finite changes which can occur in A or B without affecting the solution P of the algebraic matrix Riccati equation, and for simultaneous changes in A and B which leave both P and the optimal feedback law uk=— Kxt unaltered. If there is a predetermined variation in P, changes in A and B which leave K fixed are also given. The work complements an earlier treatment of the continuous-time case, and comparisons are noted.
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Stephen M. Barnett (1975) studied this question.
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