MATLAB tools for SM H∞ identification and guaranteed control performance computation

This paper presents two MATLAB tools called SMID (set membership identification) and GPC (guaranteed performance computation), respectively. With the SMlD tool, it is possible to perform the set membership H_∞ identification of linear, discrete-time, stable, SISO plants, obtaining additive model sets described by a linear model of given order and a magnitude-bounded perturbation accounting for the identification uncertainty due to finite samples, noisy measurements and unmodeled dynamics. When a controller C has been designed (for example using H_∞ optimization or μ-synthesis techniques, in order to exploit the previously identified model set), the GPC tool allows one to compute upper and lower bounds in the frequency domain of the main closed-loop transfer functions (sensitivity, control effort sensitivity, complementary sensitivity) for all systems belonging to the model set. The combined use of SMID tool, of user´s favorite method for robust control design and of GPC tool, allows a systematic approach to robust control design from data.