The GSS library (Generalized State Space) of the SMAC toolbox
implements a new Matlab class, which allows to model uncertain and nonlinear systems as Linear Fractional Representations. It replaces and extends the
LFR toolbox, with a more intuitive way to describe LFR and a more user-friendly interface, including a Simulink library. Several tools are proposed to manipulate GSS objects (addition, multiplication, inversion, concatenation, feedback...), obtain GSS objects from symbolic models, convert GSS/LFR/USS objects, manipulate the uncertainties and the nonlinearities (normalization, reordering, random sampling), and perform order reduction or approximation. A large class of continuous- and discrete-time systems can be handled, with real or complex uncertain or varying parameters, polytopic-type uncertain or varying elements, linear time-invariant uncertainties, sector nonlinearities, saturations, deadzones, or more general nonlinear operators. Full compatibility is also ensured with other modeling, analysis and control libraries of the SMAC toolbox (
APRICOT,
SMART,
IQC,
SAW...).