Optimal regional poles placement with time-weighted performance index

Abstract

The design of optimal discrete-time linear time-invariant systems with time-weighted performance index is studied. The optimal state feedback control law, that ensures all closed-loop poles lie inside a region H and minimizes a time-weighted performance index, is derived. The region H could be any region bounded by line segments and/or quadratic curves. The performance index consists of two parts, namely, one part is used to penalize the sustained error, while the other part is used to improve the robustness of the closed-loop system. Illustrative examples are included to demonstrate the validity and applicability of the proposed method.<>