Full-Column Rank Solutions to a Nonlinear Matrix Equation

2012 ◽  
Vol 490-495 ◽  
pp. 1265-1268 ◽  
Author(s):  
Yan Tao Wang ◽  
Xin Rong Yang ◽  
Rui Zhi Zhang
Keyword(s):  
Linear Systems ◽  
Matrix Equation ◽  
Continuous Time ◽  
Necessary Conditions ◽  
Full Rank ◽  
Full Column Rank ◽  
Nonlinear Matrix Equation ◽  
Sufficient And Necessary Conditions ◽  
Nonlinear Matrix ◽  
Descriptor Linear Systems

This paper concerns full-column rank solutions to the nonlinear matrix equation XA+XBX=HX, which is proposed from the so-called regulation problem of continuous-time (descriptor) linear systems with constrained states and controls. Sufficient and necessary conditions under which the nonlinear matrix equation has at least one full rank solution are investigated, and thereby, a mistake in [1] is pointed out by constructing a counterexample. Moreover, one full-column rank solutions to the nonlinear matrix equation is constructed.

scholarly journals Hermitian Positive Definite Solution of the Matrix Equation X=Q+∑i=1mAi(B+X-1)-1Ai*

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chun-Mei Li ◽  
Jing-Jing Peng
Keyword(s):  
Matrix Equation ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Nonlinear Matrix Equation ◽  
Positive Definite Solution ◽  
Hermitian Positive Definite Solution ◽  
The Matrix ◽  
Nonlinear Matrix ◽  
Definite Solution

We consider the Hermitian positive definite solution of the nonlinear matrix equation X=Q+∑i=1mAi(B+X-1)-1Ai*. Some new sufficient conditions and necessary conditions for the existence of Hermitian positive definite solutions are derived. An iterative method is proposed to compute the Hermitian positive definite solution. In the end, an example is used to illustrate the correctness and application of our results.

scholarly journals On the Positive Definite Solutions of a Nonlinear Matrix Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1434-1438
Author(s):  
Ming Hui Wang ◽  
Chun Yan Liang ◽  
Shan Rui Hu
Keyword(s):  
Fixed Point ◽  
Matrix Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Positive Definite ◽  
Matrix Inversion ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case are discussed. An algorithm that avoids matrix inversion with the case is proposed.

scholarly journals The iterative methods for solving nonlinear matrix equation X+A⋆X−1A+B⋆X−1B=Q

2013 ◽  
Vol 2013 (1) ◽  
pp. 229 ◽  
Author(s):  
Sarah Vaezzadeh ◽  
Seyyed Vaezpour ◽  
Reza Saadati ◽  
Choonkil Park
Keyword(s):  
Iterative Methods ◽  
Matrix Equation ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

A novel iterative method for the solution of a nonlinear matrix equation

2020 ◽  
Vol 153 ◽  
pp. 503-518 ◽  
Author(s):  
Raziyeh Erfanifar ◽  
Khosro Sayevand ◽  
Hamid Esmaeili
Keyword(s):  
Iterative Method ◽  
Matrix Equation ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix
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