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Commitdd95f35

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Merge pull request#729 from roryyorke/rory/linfnorm
ENH: add `linform` to compute linear system L-infinity norm
2 parents46b3c53 +02b3451 commitdd95f35

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2 files changed

+117
-2
lines changed

2 files changed

+117
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lines changed

‎control/statesp.py

Lines changed: 65 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -55,6 +55,7 @@
5555
fromnumpy.linalgimportsolve,eigvals,matrix_rank
5656
fromnumpy.linalg.linalgimportLinAlgError
5757
importscipyassp
58+
importscipy.linalg
5859
fromscipy.signalimportcont2discrete
5960
fromscipy.signalimportStateSpaceassignalStateSpace
6061
fromwarningsimportwarn
@@ -65,7 +66,12 @@
6566
from .importconfig
6667
fromcopyimportdeepcopy
6768

68-
__all__= ['StateSpace','tf2ss','ssdata']
69+
try:
70+
fromslycotimportab13dd
71+
exceptImportError:
72+
ab13dd=None
73+
74+
__all__= ['StateSpace','tf2ss','ssdata','linfnorm']
6975

7076
# Define module default parameter values
7177
_statesp_defaults= {
@@ -1895,3 +1901,61 @@ def ssdata(sys):
18951901
"""
18961902
ss=_convert_to_statespace(sys)
18971903
returnss.A,ss.B,ss.C,ss.D
1904+
1905+
1906+
deflinfnorm(sys,tol=1e-10):
1907+
"""L-infinity norm of a linear system
1908+
1909+
Parameters
1910+
----------
1911+
sys : LTI (StateSpace or TransferFunction)
1912+
system to evalute L-infinity norm of
1913+
tol : real scalar
1914+
tolerance on norm estimate
1915+
1916+
Returns
1917+
-------
1918+
gpeak : non-negative scalar
1919+
L-infinity norm
1920+
fpeak : non-negative scalar
1921+
Frequency, in rad/s, at which gpeak occurs
1922+
1923+
For stable systems, the L-infinity and H-infinity norms are equal;
1924+
for unstable systems, the H-infinity norm is infinite, while the
1925+
L-infinity norm is finite if the system has no poles on the
1926+
imaginary axis.
1927+
1928+
See also
1929+
--------
1930+
slycot.ab13dd : the Slycot routine linfnorm that does the calculation
1931+
"""
1932+
1933+
ifab13ddisNone:
1934+
raiseControlSlycot("Can't find slycot module 'ab13dd'")
1935+
1936+
a,b,c,d=ssdata(_convert_to_statespace(sys))
1937+
e=np.eye(a.shape[0])
1938+
1939+
n=a.shape[0]
1940+
m=b.shape[1]
1941+
p=c.shape[0]
1942+
1943+
ifn==0:
1944+
# ab13dd doesn't accept empty A, B, C, D;
1945+
# static gain case is easy enough to compute
1946+
gpeak=scipy.linalg.svdvals(d)[0]
1947+
# max svd is constant with freq; arbitrarily choose 0 as peak
1948+
fpeak=0
1949+
returngpeak,fpeak
1950+
1951+
dico='C'ifsys.isctime()else'D'
1952+
jobe='I'
1953+
equil='S'
1954+
jobd='Z'ifall(0==d.flat)else'D'
1955+
1956+
gpeak,fpeak=ab13dd(dico,jobe,equil,jobd,n,m,p,a,e,b,c,d,tol)
1957+
1958+
ifdico=='D':
1959+
fpeak/=sys.dt
1960+
1961+
returngpeak,fpeak

‎control/tests/statesp_test.py

Lines changed: 52 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -19,13 +19,15 @@
1919
fromcontrol.dtimeimportsample_system
2020
fromcontrol.ltiimportevalfr
2121
fromcontrol.statespimportStateSpace,_convert_to_statespace,tf2ss, \
22-
_statesp_defaults,_rss_generate
22+
_statesp_defaults,_rss_generate,linfnorm
2323
fromcontrol.iosysimportss,rss,drss
2424
fromcontrol.tests.conftestimportismatarrayout,slycotonly
2525
fromcontrol.xferfcnimportTransferFunction,ss2tf
2626

27+
2728
from .conftestimporteditsdefaults
2829

30+
2931
classTestStateSpace:
3032
"""Tests for the StateSpace class."""
3133

@@ -1107,3 +1109,52 @@ def test_latex_repr_testsize(editsdefaults):
11071109

11081110
gstatic=ss([], [], [],1)
11091111
assertgstatic._repr_latex_()isNone
1112+
1113+
1114+
classTestLinfnorm:
1115+
# these are simple tests; we assume ab13dd is correct
1116+
# python-control specific behaviour is:
1117+
# - checking for continuous- and discrete-time
1118+
# - scaling fpeak for discrete-time
1119+
# - handling static gains
1120+
1121+
# the underdamped gpeak and fpeak are found from
1122+
# gpeak = 1/(2*zeta*(1-zeta**2)**0.5)
1123+
# fpeak = wn*(1-2*zeta**2)**0.5
1124+
@pytest.fixture(params=[
1125+
('static',ct.tf, ([1.23],[1]),1.23,0),
1126+
('underdamped',ct.tf, ([100],[1,2*0.5*10,100]),1.1547005,7.0710678),
1127+
])
1128+
defct_siso(self,request):
1129+
name,systype,sysargs,refgpeak,reffpeak=request.param
1130+
returnsystype(*sysargs),refgpeak,reffpeak
1131+
1132+
@pytest.fixture(params=[
1133+
('underdamped',ct.tf, ([100],[1,2*0.5*10,100]),1e-4,1.1547005,7.0710678),
1134+
])
1135+
defdt_siso(self,request):
1136+
name,systype,sysargs,dt,refgpeak,reffpeak=request.param
1137+
returnct.c2d(systype(*sysargs),dt),refgpeak,reffpeak
1138+
1139+
@slycotonly
1140+
deftest_linfnorm_ct_siso(self,ct_siso):
1141+
sys,refgpeak,reffpeak=ct_siso
1142+
gpeak,fpeak=linfnorm(sys)
1143+
np.testing.assert_allclose(gpeak,refgpeak)
1144+
np.testing.assert_allclose(fpeak,reffpeak)
1145+
1146+
@slycotonly
1147+
deftest_linfnorm_dt_siso(self,dt_siso):
1148+
sys,refgpeak,reffpeak=dt_siso
1149+
gpeak,fpeak=linfnorm(sys)
1150+
# c2d pole-mapping has round-off
1151+
np.testing.assert_allclose(gpeak,refgpeak)
1152+
np.testing.assert_allclose(fpeak,reffpeak)
1153+
1154+
@slycotonly
1155+
deftest_linfnorm_ct_mimo(self,ct_siso):
1156+
siso,refgpeak,reffpeak=ct_siso
1157+
sys=ct.append(siso,siso)
1158+
gpeak,fpeak=linfnorm(sys)
1159+
np.testing.assert_allclose(gpeak,refgpeak)
1160+
np.testing.assert_allclose(fpeak,reffpeak)

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