dhinf

H_infinity design of discrete-time systems

Calling Sequence

[AK,BK,CK,DK,(RCOND)] = dishin(A,B,C,D,ncon,nmeas,gamma)

Arguments

:A the n-by-n system state matrix A. : :B the n-by-m system input matrix B. : :C the p-by-n system output matrix C. : :D the p-by-m system matrix D. : :ncon the number of control inputs. m >= ncon >= 0, p-nmeas >= ncon. : :nmeas the number of measurements. p >= nmeas >= 0, m-ncon >= nmeas. : :gamma the parameter gamma used in H_infinity design. It is

assumed that gamma is sufficiently large so that the controller is admissible. gamma >= 0.

: :AK the n-by-n controller state matrix AK. : :BK the n-by-nmeas controller input matrix BK. : :CK the ncon-by-n controller output matrix CK. : :DK the ncon-by-nmeas controller matrix DK. : :RCOND a vector containing estimates of the reciprocal condition numbers of the matrices which are to be inverted and estimates of the reciprocal condition numbers of the Riccati equations which have to be solved during the computation of the controller. (See the description of the algorithm in [1].)

:RCOND (1) contains the reciprocal condition number of the matrix R3, : :RCOND (2) contains the reciprocal condition number of the matrix R1

• R2’*inv(R3)*R2

: :RCOND (3) contains the reciprocal condition number of the matrix

V21,

: :RCOND (4) contains the reciprocal condition number of the matrix

St3,

: :RCOND (5) contains the reciprocal condition number of the matrix

V12,

: :RCOND (6) contains the reciprocal condition number of the matrix

Im2 + DKHAT*D22,

: :RCOND (7) contains the reciprocal condition number of the X-Riccati

equation,

: :RCOND (8) contains the reciprocal condition number of the Z-Riccati

equation.

:

:

Description

[AK,BK,CK,DK,(RCOND)] = dhinf(A,B,C,D,ncon,nmeas, gamma) To compute the matrices of an H-infinity (sub)optimal n-state controller

| AK | BK |
K = |----|----|,
| CK | DK |

for the discrete-time system

| A  | B1  B2  |   | A | B |
P = |----|---------| = |---|---|,
| C1 | D11 D12 |   | C | D |
| C2 | D21 D22 |

and for a given value of gamma, where B2 has column size of the number of control inputs (ncon) and C2 has row size of the number of measurements (nmeas) being provided to the controller.

References

[1] P.Hr. Petkov, D.W. Gu and M.M. Konstantinov. Fortran 77 routines for Hinf and H2 design of linear discrete-time control systems. Report99-8, Department of Engineering, Leicester University, April 1999.

Examples

//example from Niconet report SLWN1999-12
//Hinf
A=[-0.7  0    0.3  0   -0.5 -0.1
   -0.6  0.2 -0.4 -0.3  0    0
   -0.5  0.7 -0.1  0    0   -0.8
   -0.7  0    0   -0.5 -1    0
    0    0.3  0.6 -0.9  0.1 -0.4
    0.5 -0.8  0    0    0.2 -0.9];
B=[-1 -2 -2  1  0
    1  0  1 -2  1
   -3 -4  0  2 -2
    1 -2  1  0 -1
    0  1 -2  0  3
    1  0  3 -1 -2];
C=[ 1 -1  2 -2  0 -3
   -3  0  1 -1  1  0
    0  2  0 -4  0 -2
    1 -3  0  0  3  1
    0  1 -2  1  0 -2];
D=[1 -1 -2  0  0
   0  1  0  1  0
   2 -1 -3  0  1
   0  1  0  1 -1
   0  0  1  2  1];

ncon=2
nmeas=2
gam=111.30;
[AK,BK,CK,DK] = dhinf(A,B,C,D,ncon,nmeas,gam)

See Also

• hinf H_infinity design of continuous-time systems
• h_inf Continuous time H-infinity (central) controller