Stability and Stability Margin for a Two-Dimensional System

摘要

In this paper, a necessary and sufficient condition is derived for the stability of the Fornasini-Marchesini (FM) first model proposed for two-dimensional (2-D) dynamic system descriptions. A connection has been established between the stability of this model and the structured singular value (SSV) of a constant matrix, which is now widely known in control theories. Based on this connection, a novel sufficient condition is obtained for the stability of the FM first model that is more computationally convenient in filter design. Numerical simulations show that this sufficient condition is usually less conservative than that of [7]. Moreover, the stability margin of the FM first model is also investigated. It is shown that a 2-D system remains stable under parametric variations if and only if the SSV of a constant matrix is smaller than one.