# Linear Time Invariant systems¶

Linear Time Invariant systems author: S. Maraniello date: 15 Sep 2017 (still basement…)

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?