Stability of 2-D Discrete Systems in the Presence of Saturation Function and Delays

摘要

A variety of economically relevant processes are better modeled by using two-dimensional (2-D) models, which is the case, for instance, in metal rolling and the pharmaceutical industries. Typically Roesser and Fornasini Marchesini Local State Space (FMSLSS) models incorporate delayed states leading to a challenging stability analysis task. The main contribution of this work is to provide new convex stability analysis criteria for discrete-time FMSLSS models under both saturating function and time-varying delays. In particular, the saturating function tailors the digital control behavior, capturing the effect of finite wordlength. With Wirtinger and reciprocally convex sum lemmas, these new conditions can achieve less conservative results than other recent literature methods. Consequently, as illustrated by examples, this proposal enlarges the class of systems that can be stable-certified, still keep reasonable the associated computational effort.