Expand Up @@ -49,15 +49,17 @@ from .statesp import StateSpace from .statefbk import gram
__all__ = ['hsvd', 'balred', 'modred', 'era', 'markov', 'minreal'] __all__ = ['hankel_singular_values', 'balanced_reduction', 'model_reduction', 'minimal_realization', 'eigensys_realization', 'markov', 'hsvd', 'balred', 'modred', 'minreal', 'era']

# Hankel Singular Value Decomposition # # The following returns the Hankel singular values, which are singular values # of the matrix formed by multiplying the controllability and observability # Gramians def hsvd(sys): def hankel_singular_values(sys): """Calculate the Hankel singular values.
Parameters Expand Down Expand Up @@ -106,7 +108,7 @@ def hsvd(sys): return hsv[::-1]

def modred(sys, ELIM, method='matchdc'): def model_reduction(sys, ELIM, method='matchdc'): """ Model reduction of `sys` by eliminating the states in `ELIM` using a given method. Expand Down Expand Up @@ -216,7 +218,7 @@ def modred(sys, ELIM, method='matchdc'): return rsys

def balred(sys, orders, method='truncate', alpha=None): def balanced_reduction(sys, orders, method='truncate', alpha=None): """Balanced reduced order model of sys of a given order. States are eliminated based on Hankel singular value. If sys has unstable modes, they are removed, the Expand Down Expand Up @@ -340,7 +342,7 @@ def balred(sys, orders, method='truncate', alpha=None): return rsys

def minreal(sys, tol=None, verbose=True): def minimal_realization(sys, tol=None, verbose=True): ''' Eliminates uncontrollable or unobservable states in state-space models or cancelling pole-zero pairs in transfer functions. The Expand Down Expand Up @@ -368,7 +370,7 @@ def minreal(sys, tol=None, verbose=True): return sysr

def era(YY, m, n, nin, nout, r): def eigensys_realization(YY, m, n, nin, nout, r): """Calculate an ERA model of order `r` based on the impulse-response data `YY`.
Expand Down Expand Up @@ -556,3 +558,10 @@ def markov(Y, U, m=None, transpose=False):
# Return the first m Markov parameters return H if transpose else np.transpose(H)
# Function aliases hsvd = hankel_singular_values balred = balanced_reduction modred = model_reduction minreal = minimal_realization era = eigensys_realization