This paper is concerned with the positive definite solutions to the nonlinear matrix equation
X+ AHX¯-1A= I where X is the unknown and A is a given complex matrix. By introducing and …

This paper studies the iterative solutions of Lyapunov matrix equations associated with Itô
stochastic systems having Markovian jump parameters. For the discrete-time case, when the …

Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to
functions useful in control theory systems, basis functions in numerical methods or …

In this paper, the sensitivity of the solution to the general type nonlinear matrix equation
C+∑ ki= 1 σiA∗ i Xpi Ai= 0, σi=±1 is studied, where k is a positive integer and pi, i= 1,... k are …

In this paper, we consider a nonlinear matrix equation, which has the form, where is a
positive integer, is an arbitrary complex matrix and is an Hermitian positive definite matrix. A …

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 …

In this paper, the distribution of the positive definite solution of the nonlinear equation X s+
A∗ Xq A= I is deduced, the existence of the maximal solution and the minimal solution is …

In this chapter, we consider Hermitian polynomial matrix equations X s±∑ i= 1 ℓ δ i A i∗ X ti
A i= Q, which frequently arise from linear-quadratic control problems. The latest results of …

The nonlinear matrix equations X±A∗ X− 1A= Q have many applications in control theory,
dynamic programming and statistics. In the present work, by using some related matrix …

This paper is concerned with the positive definite solutions to the matrix equation $ X+
A^{\mathrm {H}}\bar {X}^{-1} A= I $ where $ X $ is the unknown and $ A $ is a given complex …