lqe (MathScript RT Module Function)

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Owning Class: ssdesign

Requires: Control Design and Simulation Module and MathScript RT Module

Syntax

[L, X, eig] = lqe(A, G, C, Q, R)

[L, X, eig] = lqe(A, G, C, Q, R, N)

[L, X, eig] = lqe(SysSS, G, Q, R)

[L, X, eig] = lqe(SysSS, G, Q, R, N)

Calculates the optimal steady-state estimator gain matrix L for a continuous state-space model defined by matrices A and C.

Name	Description
A	Specifies an n x n state matrix, where n is the number of states. The default is an empty matrix. A is a real matrix.
G	Specifies a matrix that relates the process noise to the states.
C	Specifies an r x n output matrix, where r is the number of outputs. C is a real matrix.
Q	Specifies a symmetric, positive semi-definite matrix that penalizes the state vector x in the cost function. Q is a real matrix.
R	Specifies a symmetric positive definite matrix that penalizes the output vector y in the cost function. The default is the identity matrix. R is a real matrix.
N	Specifies a matrix that penalizes the cross product between output and state vectors, such that (Q - Ninv(R)N') is positive semi-definite. The default is an appropriately-sized matrix of zeros. N is a real matrix.
SysSS	Specifies a linear time-invariant (LTI) model in state-space form.

Name	Description
L	Returns the Kalman gain matrix. L is a real matrix.
X	Returns the symmetric, positive semi-definite (stabilizing) solution to the discrete algebraic Riccati equation. X is a real matrix.
eig	Returns the eigenvalues of the matrix (A - LC). These eigenvalues are the closed-loop pole locations. eig is a complex vector.

The following table lists the support characteristics of this function.

Supported in the LabVIEW Run-Time Engine	Yes
Supported on RT targets	Yes
Suitable for bounded execution times on RT	Not characterized

A = [-1, -2; 0, -4];
G = eye(2)
C = [0; 1];
Q = [2, 0; 0, 2];
R = 1;
[L, X, eig] = lqe(A, G, C, Q, R)