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【期刊论文】Nonlinear systems possessing linear symmetry
杨国武, Daizhan Cheng*, y, Guowu Yang and Zairong Xi
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2007; 17: 51-81,-0001,():
-1年11月30日
This paper tackles linear symmetries of control systems. Precisely, the symmetry of affine nonlinear systems under the action of a sub-group of general linear group GL?n;R?: First of all, the structure of state space (briefly, ss) symmetry group and its Lie algebra for a given system is investigated. Secondly, the structure of systems, which are ss-symmetric under rotations, is revealed. Thirdly, a complete classification of ss-symmetric planar systems is presented. It is shown that for planar systems there are only four classes of systems which are ss-symmetric with respect to four linear groups. Fourthly, a set of algebraic equations are presented, whose solutions provide the Lie algebra of the largest connected ss-symmetry group. Finally, some controllability properties of systems with ss-symmetry group are studied. As an auxiliary tool for computation, the concept and some properties of semi-tensor product of matrices are included. Copyright
linear symmetry, Lie group, Lie algebra, control system, semi-tensor product of matrices
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【期刊论文】Majority-based reversible logic gates
杨国武, GuowuYang, William N.N. Hung?, Xiaoyu Song, Marek Perkowski
Theoretical Computer Science 334(2005)259-274,-0001,():
-1年11月30日
Reversible logic plays an important role in the synthesis of circuits for quantum computing. In this paper, we introduce families of reversible gates based on the majority Boolean function (MBF) and we prove their properties in reversible circuit synthesis. These gates can be used to synthesize reversible circuits of minimum "scratchpad register width" for arbitrary reversible functions.We show that, given a MBF f with 2k+1 inputs, f can be implemented by a reversible logic gate with 2k+1 inputs and 2k+1 outputs, i.e., without any constant inputs.We also demonstrate new gates from this family with very efficient quantum realizations for majority-based applications. They can be used to synthesize any reversible function of the same width in conjunction with inverters and Feynman (2-qubit controlled-NOT) gates. The gate universality problem is formulated in terms of elementary group theory and solved using the algebraic software GAP.
Reversible logic, Quantum computing, Majority Boolean functions, Logic synthesis
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