Data-driven stability margin for linear multivariable systems

The notion of stability margin (SM) plays an important role in control engineering. For multiple-input multiple-output (MIMO) systems, the classic SM is no longer applicable. The one-loop-at-a-time analysis method may lead to unreliable SMs. Although some robust SM analysis methods are popular in MIMO systems, they are model-based or not easy-to-use in engineering sometimes. In this paper, & Laplacetrf;2$$ {\mathcal{L}}_2 $$ gain margin and & Laplacetrf;2$$ {\mathcal{L}}_2 $$ time-delay margin are defined for linear MIMO systems, and a corresponding SM analysis method is proposed by utilizing a loop transformation and the small-gain theorem. Most importantly, a data-driven method for measuring the defined SMs is also presented. As a frequency-domain method, this method can be used to experimentally obtain the SMs of MIMO systems on model-free occasions. The proposed SM analysis method and measurement method are simple and practical. Two simulation studies and an experimental test are performed to illustrate the effectiveness and practicability of the proposed method.