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Evaluation of the impulsive solution space of linear multivariable homogeneous implicit systems. (English) Zbl 0832.93031
A linear homogeneous matrix differential equation is a differential equation \(A(d/dt) x(t)= 0\), where \(A(s)\) is a matrix polynomial. A classical formula is given which allows the determination of the impulsive solutions of linear homogeneous matrix differential equations directly in terms of finite and infinite spectral data of the associated polynomial matrix. The notions of finite and infinite Jordan pairs are defined for a general polynomial matrix and the strong relationship between them and the impulsive solutions of linear homogeneous matrix differential equations are pointed out.
MSC:
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
93B60 Eigenvalue problems
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