Semi-tensor product of matrices and its application to Morgen’s problem
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This paper proposes a new matrix product, namely, semi-tensor product. It is a generalization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional data; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgen’s problem for control systems is formulated as a numerically solvable problem.
[1] Tatsushi Ooba,et al. Two conditions concerning common quadratic Lyapunov functions for linear systems , 1997, IEEE Trans. Autom. Control..
[2] J. Descusse,et al. Solution to Morgan's problem , 1988 .
[3] Nobuhide Suda,et al. Decoupling of Nonsquare Systems — a Necessary and Sufficient Condition in Terms of Infinite Zeros , 1984 .