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hinfsyn 259
1. (a,b
2
,c
2
) is stabilizable and detectable
2. d
12
and d
21
have full rank
3. The matrix [a − jωI,b
2
;c
1
,d
12
] has full column rank for all ω
4. The matrix [a − jωI,b
1
;c
2
,d
21
] has full row rank for all ω
Reference
This function uses the state-space formulae given in:
“State-space formulae for all stabilizing controllers that satisfy an H
∞
norm bound and
relations to risk sensitivity,” Keith Glover and John Doyle, Systems & Control Letters
11, pp. 167–172., Oct, 1988.
Example
# Set up a simple closed loop problem.
# A tracking problem is chosen. Weights are used to
# trade off between tracking performance and actuator
# effort.
plant = makepoly([0.1,-0.1,1],"s")*makepoly([1,1],"s")...
/(makepoly([1,0.1,.1],"s")*(makepoly([0.2,1],"s")))
# Create weights (performance & actuator)
Wperf = 100/makepoly([100,1],"s")
Wact = makepoly([0.5,0.05],"s")/makepoly([0.05,1],"s")
# Form the weighted interconnection structure
sysnames = ["plant";"Wperf";"Wact"]
sysinp = ["ref";"control"]
sysout = ["Wperf"; "Wact"; "ref-plant"]
syscnx = ["control"; ... # input to plant
"ref-plant"; ... # input to Wperf
"control"] # input to Wact