Continuity properties of l1/L1-optimal controllers for plants with stability-boundary zeros

Continues the study of nonstandard l₁/L₁ optimal control problems. The main result shows that in the discrete time case the l₁ optimal-cost is not continuous when the zeros of the plant move continuously on the unit circle. Surprisingly, in the continuous time counterpart, the L¹ optimal cost changes continuously as the zeros of the plant move on the jω-axis. The paper is organized as follows: in section 2 the authors introduce the notation and definitions to be used, briefly state the l₁ optimal control problem and review the solution to the standard problem; in section 3 the authors consider l₁ problems for plants having zeros on the unit circle and show that the l ₁ optimal cost is not continuous on the unit circle; in section 4 the authors consider nonstandard L¹ 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