Positive real control for uncertain two-dimensional systems

• DOI: 10.1109/tcsi.2002.804531
• Publication Date: 2003-01-03T17:55:00Z
• Authors: Shengyuan Xu; J. Lam; Zhiping Lin; K. Galkowski
• Keywords: 0209 industrial biotechnology; Positive realness; 515; Fornasini-Marchesini local state-space (FMLSS) model; Linear matrix inequality (LMI); State feedback; 02 engineering and technology; Two-dimensional (2-D) systems

This brief deals with the problem of positive real control for uncertain two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini local state-space model. The parameter uncertainty is time-invariant and norm-bounded. The problem we address is the design of a state feedback controller that robustly stabilizes the uncertain system and achieves the extended strictly positive realness of the resulting closed-loop system for all admissible uncertainties. A version of positive realness for 2-D discrete systems is established. Based on this, a condition for the solvability of the positive real control problem is derived in terms of a linear matrix inequality. Furthermore,the solution of a desired state feedback controller is also given. Finally, we provide a numerical example to demonstrate the applicability of the proposed approach.