Positive real control for uncertain two-dimensional systems

By Shengyuan Xu, James Lam, Zhiping Lin, K. Gałkowski. 2002

83 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e648ca69a819ec8121ce3c588391820a0a50a02c