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Systems modeling

The GSS library (Generalized State Space) is the core of the SMAC Toolbox. It 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...).

The APRICOT library (Approximation of Polynomial and Rational-type for Indeterminate Coefficients via Optimization Tools) is an optional module, which is compatible with both the GSS library and the LFR toolbox. It allows to convert a set of scalar, vector or matrix samples into sparse polynomial or rational expressions, for which the number of terms in the numerator and denominator is as low as possible. Simple yet accurate LFR are obtained, which are tractable both for analysis and design purposes.

Note that the LFR toolbox (Linear Fractional Representation) is not maintained anymore since 2014, but its latest version can still be downloaded.