Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS
Volume 49, Issue 11, Pages 1659-1666Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2002.804531
Keywords
Fornasini-Marchesini local state-space (FMLSS) model; linear matrix inequality (LMI); positive realness; state feedback; two-dimensional (2-D) systems
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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.
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