matrix algebraoptimal controlminimizationperformance analysisThe aim of this paper is to determine an explicit solution of the Lyapunov equation by using the arrow form matrix. The main result points out that, if the unknown matrix is (n x n), the solution can be determined through the ...
百度试题 结果1 题目The solution of the matrix equation is X=A^(-1)B. 相关知识点: 试题来源: 解析反馈 收藏
Solution of the matrix equation AX + XB = C [F4] Anis not available. RH Bartels,G W Stewart - 《Communications of the Acm》 被引量: 940发表: 1972年 Solution of the Matrix Equation AX-XB=C The solution of linear matrix equation AX-XB=C often appears in the control theory,in the li...
Purpose The purpose of this paper is to study the existence and uniqueness of a positive definite solution to the nonlinear matrix equation X = Q − A ∗ X −1 A + B ∗ X −1 B, which is a special stochastic rational Riccati equation arising in stochastic control theory. Methods...
摘要: Let A λB and C λD be two normal matrix pencils or Hermitian matrix pencils or definite matrix pencils, and let AXD BXC = S. Our main results in this part are estimates of a unitarily invariant norm of the solution X under some conditions on the spectra of two pencils. §...
,N, where vi(j) is the i-component of vector v̲(j). Then, if The analogue of the implicit equation (4) Starting with the spectral solution of (5) obtained in the previous section, it is possible to construct, if ρ=ρ˜=0, the matrix analogue of the implicit non-differential...
Similarly, the matrix representation of y3(x) becomes (11) where (12) Finally, by substituting the matrix forms (4)–(11) into (1) we have the fundamental matrix equation (13) 3. Method of the Solution To obtain the Taylor polynomial solution of (1) in the form (3) we firstly...
The purpose of this paper is to study the existence and uniqueness of a positive definite solution to the nonlinear matrix equation X = Q − A∗X −1A + B∗X −1B, which is a special stochastic rational Riccati equation arising in stochastic control theory. Methods Ou...
The unique solution of the matrix equation AXB CXD = E is obtained in explicit form by means of the inversion of an n X n or m X m matrix from the coefficients of the Laurent expansions of ( λC A) 1 and ( λB D) 1 and the relative characteristic polynomial of λC A or λB...
Solution of Linear Systems Systems of Linear Equations Consider the linear system Ax = b where A is an (n x n) matrix, x is the vector of (n) unknown solution values, and b is a column vector of constants Solution of a Linear System A formal way to obtain a solution using matrix ...