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control.h2syn — Python Control Systems Library 0.10.2 documentation

control.h2syn(P, nmeas, ncon)[source]

H2 control synthesis for plant P.

Parameters:

PStateSpace

Partitioned LTI plant (state-space system).

nmeasint

Number of measurements (input to controller).

nconint

Number of control inputs (output from controller).

Returns:

KStateSpace

Controller to stabilize P.

Raises:

ImportError

If slycot routine sb10hd is not loaded.

Examples

>>> # Unstable first order SISO system
>>> G = ct.tf([1], [1, -1], inputs=['u'], outputs=['y'])
>>> all(G.poles() < 0)  # Is G stable?
False

>>> # Create partitioned system with trivial unity systems
>>> P11 = ct.tf([0], [1], inputs=['w'], outputs=['z'])
>>> P12 = ct.tf([1], [1], inputs=['u'], outputs=['z'])
>>> P21 = ct.tf([1], [1], inputs=['w'], outputs=['y'])
>>> P22 = G
>>> P = ct.interconnect([P11, P12, P21, P22],
...                     inplist=['w', 'u'], outlist=['z', 'y'])

>>> # Synthesize H2 optimal stabilizing controller
>>> K = ct.h2syn(P, nmeas=1, ncon=1)
>>> T = ct.feedback(G, K, sign=1)
>>> all(T.poles() < 0)  # Is T stable?
True

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