— Function File: [k, g, gw, xinf, yinf] = hinfsyn (asys, nu, ny, gmin, gmax, gtol, ptol, tol)

Inputs input system is passed as either

asys

system data structure (see ss, sys2ss)

• controller is implemented for continuous time systems
• controller is not implemented for discrete time systems (see bilinear transforms in c2d, d2c)

nu

number of controlled inputs

ny

number of measured outputs

gmin

initial lower bound on H-infinity optimal gain

gmax

initial upper bound on H-infinity Optimal gain.

gtol

Gain threshold. Routine quits when gmax/gmin < 1+tol.

ptol

poles with abs(real(pole)) < ptol*||H|| (H is appropriate Hamiltonian) are considered to be on the imaginary axis. Default: 1e-9.

tol

threshold for 0. Default: 200*eps.

gmax, min, tol, and tol must all be positive scalars.

Outputs

k

System controller.

g

Designed gain value.

gw

Closed loop system.

xinf

ARE solution matrix for regulator subproblem.

yinf

ARE solution matrix for filter subproblem.

References:

1. Doyle, Glover, Khargonekar, Francis, State-Space Solutions to Standard H-2 and H-infinity Control Problems, IEEE TAC August 1989.
2. Maciejowksi, J.M., Multivariable feedback design, Addison-Wesley, 1989, ISBN 0-201-18243-2.
3. Keith Glover and John C. Doyle, State-space formulae for all stabilizing controllers that satisfy an H-infinity-norm bound and relations to risk sensitivity, Systems & Control Letters 11, Oct. 1988, pp 167–172.