qttools.lyapunov.utils#

Functions

system_reduction — Computes the solution of the discrete-time Lyapunov equation.

source system_reduction(a: NDArray, q: NDArray, contact: str, solve, out: None | NDArray = None)

Computes the solution of the discrete-time Lyapunov equation.

The system is reduced by rows of A (AXA^H - X + Q = 0) that are all zero. This results in a system which is only of size n x n, where n is the number of rows with non-zero elements.

The matrices a and q can have different ndims with q.ndim >= a.ndim (will broadcast)

Parameters

a : NDArray — The system matrix.
q : NDArray — The right-hand side matrix.
contact : str — The contact to which the boundary blocks belong.
solve : function — The solver to use for the reduced system.
out : NDArray, optional — The array to store the result in. If not provided, a new array is returned.

Returns

x : NDArray | None — The solution of the discrete-time Lyapunov equation.