Continuity properties of l/sub 1//L/sub 1/-optimal controllers for plants with stability-boundary zeros

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Abstract
Continues the study of nonstandard l/sub 1//L/sub 1/ optimal control problems. The main result shows that in the discrete time case the l/sub 1/ optimal-cost is not continuous when the zeros of the plant move continuously on the unit circle. Surprisingly, in the continuous time counterpart, the L/sup 1/ optimal cost changes continuously as the zeros of the plant move on the j/spl omega/-axis. The paper is organized as follows: in section 2 the authors introduce the notation and definitions to be used, briefly state the l/sub 1/ optimal control problem and review the solution to the standard problem; in section 3 the authors consider l/sub 1/ problems for plants having zeros on the unit circle and show that the l/sub 1/ optimal cost is not continuous on the unit circle; in section 4 the authors consider nonstandard L/sup 1/ optimal control problems for continuous time systems, and show that a similar discontinuity no longer exists; and finally the authors conclude with some final remarks.

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