dlyap {netcontrol}

Discrete Lyapunov Equation Solver

Description

Computes the solution of AXA^T - X + W = 0 using the Barraud 1977 approach, adapted from Datta 2004. This implementation is equivalent to the Matlab implementation of dylap.

Usage

dlyap(A, W)

Arguments

A

n x n numeric or complex matrix.

W

n x n numeric or complex matrix.

Value

The solution to the above Lyapunov equation.

References

Barraud A (1977). “A numerical algorithm to solve \$ A^TXA - X = Q\$.” IEEE Transactions on Automatic Control, 22(5), 883–885. ISSN 0018-9286, doi: 10/fr9gs7, http://ieeexplore.ieee.org/document/1101604/.

Datta BN (2004). Numerical methods for linear control systems: design and analysis. Elsevier Academic Press, Amsterdam ; Boston. ISBN 978-0-12-203590-6.

Examples

A = matrix(c(0,-3,-2,2,-2,1,-1,2,-1), 3,3)
C = matrix(c(-2,-8,11,2,-6,13,-3,-5,-2), 3,3)
X = dlyap(t(A), C)

print(sum(abs(A %*% X %*% t(A) - X + C)))