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Positive real control for uncertain two-dimensional systems

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4 Author(s)
Shengyuan Xu ; Center for Syst. Eng. & Appl. Mech., Univ. Catholique de Louvain, Louvain-la-Neuve, Belgium ; Lam, J. ; Zhiping Lin ; Galkowski, K.

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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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:49 ,  Issue: 11 )