lqe

Kalman estimator design for continuous-time systems.

Syntax

• [L, P, E] = lqe(A, G, C, Q, R, N)
• [L, P, E] = lqe(A, G, C, Q, R)

Input argument

• A - State matrix: n x n matrix.
• G - Defines a matrix linking the process noise to the states.
• C - The output matrix, with dimensions (q x n), where q is the number of outputs.
• Q - State-cost weighted matrix
• R - Input-cost weighted matrix
• N - Optional cross term matrix: 0 by default.

Output argument

• L - Kalman gain matrix.
• P - Solution of the Discrete Algebraic Riccati Equation.
• E - Closed-loop pole locations

Description

The function computes the optimal steady-state feedback gain matrix, denoted as L, minimizing a quadratic cost function for a linear discrete state-space system model.

Example

c = 1;
m = 1;
k = 1;
A = [0, 2; -k/m, -c/m];
B = [0; 2/m];
G = [2 0 ; 0 2];
C = [2 0];
Q = [0.02 0; 0 0.02];
R = 0.02;
[l, p, e] = lqe(A, G, C, Q, R)

See also

lqr.

History

Author

Allan CORNET