A structured condition number for self-adjoint polynomial matrix equations with applications in linear control

2018 ◽  
Vol 331 ◽  
pp. 208-216 ◽  
Author(s):  
Zhi-Gang Jia ◽  
Mei-Xiang Zhao
Keyword(s):  
Condition Number ◽  
Polynomial Matrix ◽  
Linear Control ◽  
Matrix Equations ◽  
Adjoint Polynomial

On Polynomial Matrix Equations

1986 ◽  
Vol 17 (5) ◽  
pp. 388 ◽  
Author(s):  
Harley Flanders
Keyword(s):  
Polynomial Matrix ◽  
Matrix Equations

scholarly journals Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhigang Jia ◽  
Meixiang Zhao ◽  
Minghui Wang ◽  
Sitao Ling
Keyword(s):  
Iterative Algorithm ◽  
Perturbation Analysis ◽  
Matrix Equation ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Polynomial Matrix ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Solvability Theory ◽  
Adjoint Polynomial

The solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.

Kronecker Maps and Sylvester-Polynomial Matrix Equations

2007 ◽  
Vol 52 (5) ◽  
pp. 905-910 ◽  
Author(s):  
Ai-Guo Wu ◽  
Guang-Ren Duan ◽  
Yu Xue
Keyword(s):  
Polynomial Matrix ◽  
Matrix Equations

scholarly journals Solving systems of matrix equations of the second degree

2021 ◽  
pp. 52-56
Author(s):  
Anastasiya Nedashkovska
Keyword(s):  
Optimization Problems ◽  
Polynomial Matrix ◽  
Theoretical Calculations ◽  
System Optimization ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Real Numbers ◽  
Universal Approach ◽  
Matrix Fraction ◽  
Second Degree

Matrix equations and systems of matrix equations are widely used in control system optimization problems. However, the methods for their solving are developed only for the most popular matrix equations – Riccati and Lyapunov equations, and there is no universal approach for solving problems of this class. This paper summarizes the previously considered method of solving systems of algebraic equations over a field of real numbers [1] and proposes a scheme for systems of polynomial matrix equations of the second degree with many unknowns. A recurrent formula for fractionalization a solution into a continued matrix fraction is also given. The convergence of the proposed method is investigated. The results of numerical experiments that confirm the validity of theoretical calculations and the effectiveness of the proposed scheme are presented.

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