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lqed

Calculates the discrete Kalman estimator configuration based on a continuous cost function.

Syntax

[L, P, Z, E] = LQED(A, G, C, Q, R, Ts)

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.

Ts

sample time: scalare.

Output argument

L

Kalman gain matrix.

P

Solution of the Discrete Algebraic Riccati Equation.

E

Closed-loop pole locations

Z

Discrete estimator poles

Description

[L, P, Z, E] = LQED(A, G, C, Q, R, Ts) Calculates the discrete Kalman gain matrix L to minimize the discrete estimation error, equivalent to the estimation error in the continuous system.

Example

A = [10     1.2;  3.3     4];
B = [5     0;   0     6];
C = B;
D = [0,0;0,0];
R = [2,0;0,3];
Q = [5,0;0,4];
G = [6,0;0,7];
Ts = 0.004;

[L, P, Z, E] = lqed(A, G, C, Q, R, Ts)

See also

lqr, lqe.

History

Version Description
1.0.0 initial version

Author

Allan CORNET

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