INFINITE-HORIZON LINEAR-QUADRATIC CONTROL WITH END-POINT STATE PENALTY TERM - THE DISCRETE-TIME CASE

For a given discrete-time system, consider an infinite-horizon linear- quadratic control problem with positive semidefinite cost criterion an d an extra penalty term for the state variable at infinity. Our centra l result shows that this problem is structurally equivalent to the ass ociated problem, where the state penalty term is required to vanish at infinity, provided only that the latter problem has finite optimal co st everywhere. For this case, the optimal cost is represented by a uni que solution of the (possibly singular) algebraic Riccati equation, an d if, in addition, the underlying system is left-invertible, then opti mal inputs for either problem are implementable as state feedback laws , expressed in terms of the original system coefficients only, even wh en the control weighting matrix in the cost criterion is not invertibl e. (C) Elsevier Science Inc., 1997.