General idea: Solve (4.9b)-(4.9d) explic- itly. Insert the solution into (4.9a) and repeat the process for the smaller equa- tion which is a Lyapunov equation ...

5 сент. 2012 г. · All Lyapunov equations AX+XAT=B have a unique, symmetric solution X=XT, unless there is a λ∈C such that λ and −λ are both eigenvalues of A. This ...

For the discrete case, the Schur method of Kitagawa is often used. For the continuous Lyapunov equation the Bartels–Stewart algorithm can be used.

Solving the Lyapunov equation. A. T. P + PA + Q = 0 we are given A and Q and want to find P if Lyapunov equation is solved as a set of n(n + 1)/2 equations in.

2 дек. 2017 г. · Here equation (3.12) is PA+ATP=−Q. How is the 3×3 matrix on the left-side of the first matrix equation formed? linear algebra - Special case of Lyapunov equation $AP+PA=-I Solving lyapunov equation, Matlab has different solution, why? Другие результаты с сайта math.stackexchange.com

Use lyap to solve the special and general forms of the Lyapunov equation. Lyapunov equations arise in several areas of control, including stability theory.

The equation, with a negative definite, yields a unique positive definite solution if and only if the eigenvalues of are in the closed left half-plane.

The most numerically effective method (The Schur method, described in Chapter 8), for solving a Lyapunov matrix equation is based on reduction of the matrix A ...

20 нояб. 2018 г. · Equilibrium points of the differential Lyapunov equation, namely solutions of the algebraic Lyapunov equation, are used to construct quadratic ...

The continuous Lyapunov equation is a special form of the Sylvester equation, hence this solver relies on LAPACK routine ?TRSYL. Added in version 0.11.0.