Differential calculus for the matrix norms |·|1 and |·|∞ with applications to asymptotic bounds for periodic linear systems

2004 ◽  
Vol 81 (1) ◽  
pp. 81-101 ◽  
Author(s):  
L. Kohaupt
Keyword(s):  
Linear Systems ◽  
Differential Calculus ◽  
Asymptotic Bounds ◽  
Periodic Linear ◽  
The Matrix ◽  
Matrix Norms

On Stability of Linear Systems with Impulsive Action at the Matrix

2018 ◽  
Vol 230 (5) ◽  
pp. 673-676 ◽  
Author(s):  
N. I. Zhelonkina ◽  
A. N. Sesekin
Keyword(s):  
Linear Systems ◽  
Impulsive Action ◽  
The Matrix

DMRG Approach to Fast Linear Algebra in the TT-Format

2011 ◽  
Vol 11 (3) ◽  
pp. 382-393 ◽  
Author(s):  
Ivan Oseledets
Keyword(s):  
Linear Systems ◽  
Linear Algebra ◽  
Direct Method ◽  
Fast Algorithms ◽  
Approximate Solutions ◽  
Vector Product ◽  
The Matrix ◽  
Minimization Scheme

AbstractIn this paper, the concept of the DMRG minimization scheme is extended to several important operations in the TT-format, like the matrix-by-vector product and the conversion from the canonical format to the TT-format. Fast algorithms are implemented and a stabilization scheme based on randomization is proposed. The comparison with the direct method is performed on a sequence of matrices and vectors coming as approximate solutions of linear systems in the TT-format. A generated example is provided to show that randomization is really needed in some cases. The matrices and vectors used are available from the author or at http://spring.inm.ras.ru/osel

Solutions to the matrix equation X − AXB = CY+R and its application

2016 ◽  
Vol 40 (3) ◽  
pp. 995-1004 ◽  
Author(s):  
Caiqin Song ◽  
Guoliang Chen
Keyword(s):  
Linear Systems ◽  
Matrix Equation ◽  
Controller Design ◽  
Equivalent Form ◽  
Closed Form Solutions ◽  
Lyapunov Matrix Equation ◽  
Special Cases ◽  
The Matrix ◽  
Lyapunov Matrix ◽  
Low Dimensional

The solution of the nonhomogeneous Yakubovich matrix equation [Formula: see text] is important in stability analysis and controller design in linear systems. The nonhomogeneous Yakubovich matrix equation [Formula: see text], which contains the well-known Kalman–Yakubovich matrix equation and the general discrete Lyapunov matrix equation as special cases, is investigated in this paper. Closed-form solutions to the nonhomogeneous Yakubovich matrix equation are presented using the Smith normal form reduction. Its equivalent form is provided. Compared with the existing method, the method presented in this paper has no limit to the dimensions of an unknown matrix. The present method is suitable for any unknown matrix, not only low-dimensional unknown matrices, but also high-dimensional unknown matrices. As an application, parametric pole assignment for descriptor linear systems by PD feedback is considered.

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