Common solution to the Lyapunov equation for 2×2 complex matrices
نویسندگان
چکیده
منابع مشابه
The perturbation bound for the solution of the Lyapunov equation ∗
We present the first order error bound for the Lyapunov equation AX +XA∗ = −GG∗, where A is perturbed to A+ δA. We use the structure of the solution of the Lyapunov equation X = m ∑ k=1 WkW ∗ k , where Wk is the k-th matrix obtained by the Low Rank Cholesky Factor ADI (LRCF-ADI) algorithm using the set of ADI parameters equal to exact eigenvalues of A, that is with ADI parameters {p1, . . . , p...
متن کاملBounds for the solution of the discrete algebraic Lyapunov equation
New bounds for solutions of the discrete algebraic Lyapunov equation P = APA T + Q are derived. The new bounds are compared to existing ones and found to be of particular interest when A is non-normal.
متن کاملNumerical Solution of the Stable, Non-negative Definite Lyapunov Equation
is called the continuous-time Lyapunov equation and is of interest in a number of areas of control theory such as optimal control and stability (Barnett, 1975; Barnett & Storey, 1968). The equation has a unique Hermitian solution, X, if and only if Xt + X~j ^ 0 for all i and j (Barnett, 1975). In particular if every Xt has a negative real part, so that A is stable, and if C is non-negative defi...
متن کاملLyapunov equation
This chapter is about numerical methods for a particular type of equation expressed as a matrix equality. The Lyapunov equation is the most common problem in the class of problems called matrix equations. Other examples of matrix equations: Sylvester equation, Stein equation, Riccati equation. Definition 5.0.1 Consider two square matrices A, W ∈ Rn×n. The problem to find a square matrix X ∈ Rn×...
متن کاملBounds on the trace of a solution to the Lyapunov equation with a general stable matrix
Some new estimates for the eigenvalue decay rate of the Lyapunov equation AX + XA = B with a low rank right-hand side B are derived. The new bounds show that the right-hand side B can greatly influence the eigenvalue decay rate of the solution. This suggests a new choice of the ADI-parameters for the iterative solution. The advantage of these new parameters is illustrated on second order damped...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.08.028