# Linear Time Invariant systemsÂ¶

Linear Time Invariant systems author: S. Maraniello date: 15 Sep 2017 (still basementâ€¦)

Library of methods to build/manipulate state-space models. The module supports the sparse arrays types defined in libsparse.

The module includes:

Classes: - ss: provides a class to build DLTI/LTI systems with full and/or sparse

matrices and wraps many of the methods in these library. Methods include: - freqresp: wraps the freqresp function - addGain: adds gains in input/output. This is not a wrapper of addGain, as the system matrices are overwritten

Methods for state-space manipulation: - couple: feedback coupling. Does not support sparsity - freqresp: calculate frequency response. Supports sparsity. - series: series connection between systems - parallel: parallel connection between systems - SSconv: convert state-space model with predictions and delays - addGain: add gains to state-space model. - join2: merge two state-space models into one. - join: merge a list of state-space models into one. - sum state-space models and/or gains - scale_SS: scale state-space model - simulate: simulates discrete time solution - Hnorm_from_freq_resp: compute H norm of a frequency response - adjust_phase: remove discontinuities from a frequency response

Special Models: - SSderivative: produces DLTI of a numerical derivative scheme - SSintegr: produces DLTI of an integration scheme - build_SS_poly: build state-space model with polynomial terms.

Filtering: - butter

Utilities: - get_freq_from_eigs: clculate frequency corresponding to eigenvalues

Comments: - the module supports sparse matrices hence relies on libsparse.

- to do:
remove unnecessary coupling routines

- couple function can handle sparse matrices but only outputs dense matrices
verify if typical coupled systems are sparse

update routine

add method to automatically determine whether to use sparse or dense?