線形むだ時間システムにおけるL²ゲイン解析と状態フィードバック制御

無限次元LMIアプローチ

抄録

In this paper, we propose a new method of L²-gain analysis and state feedback control synthesis for time-delay systems via infinite-dimensional LMI, which reflects explicitly infinite-dimensionality features of time-delay systems. First, we show an infinite-dimensional LMI condition for L²-gain analysis. The infinite-dimensional LMI condition depends two parameters, and difficult to solve. Next, we propose a method of solving such infinite-dimensional LMI conditions using a convex polyhedron. The method consists of two steps: the first step is to make a convex polyhedron, and the second step is to reduce an infinite-dimensional LMI condition to a finite-dimensional LMI condition using the convex polyhedron. Finally, we discuss a state-feedback control synthesis based on the infinite-dimensional LMI conditions for L²-gain analysis and the method of solving infinite-dimensional LMIs, when the feedback gain is constrained.