I’m excited to share our new preprint on robust stabilization, by Saman Cyrus and me. The title is “Generalized necessary and sufficient robust boundedness results for feedback systems”, and it is now available on arXiv. This work is the culmination of Saman’s PhD and formed the core of his thesis, which he recently successfully defended (!).
Robust stabilization is an old problem, dating back at least 70 years to the seminal work of Lur’e, Zames, and Willems. The basic idea is that a known system G is in feedback with an unknown nonlinearity H constrained to lie in some known set, and we seek sufficient conditions on G that ensure stability of the interconnection. In this work, we looked at the case where the nonlinearity is constrained to lie in a cone (also known as “sector-bounded”). Results of this type include: small-gain, circle, passivity, and extended conicity. It may be possible to extend our ideas to dynamic versions of robust stability (multiplier theory, dissipativity, or integral quadratic constraints), but this is an area for future work.
Continue reading →