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

Version	📄 Description
1.0.0	initial version