Disturbance decoupling of mix-valued logical networks via the semi-tensor product method

Authors:
Zhenbin Liu;Yuzhen Wang
Affiliations:
School of Control Science and Engineering, Shandong University, Jinan 250061, PR China and School of Science and Information Science, Qingdao Agricultural University, Qingdao 266109, PR China;School of Control Science and Engineering, Shandong University, Jinan 250061, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

This paper addresses the disturbance decoupling problem (DDP) of mix-valued logical networks by using both the semi-tensor product of matrices and the matrix expression of logical functions, and presents a number of new results on the DDP. First, in order to solve the DDP, a new algorithm is proposed to construct a kind of Y-friendly subspace for the state space of mix-valued logical networks. Second, based on the constructed Y-friendly subspace, several necessary and sufficient conditions are obtained for the existence of decoupling controllers, and a new control design procedure is established to deal with the DDP. Finally, an illustrative example is studied by the new method proposed in this paper, and two kinds of decoupling controllers are designed. The study of the illustrative example shows that the new method is effective in dealing with the DDP of mix-valued logical networks.