The paper considers the long-standing open problem of static output feedback stabilization with periodic output feedback. Extending the tools from vibrational control theory, we are able to derive some original results for this problem. We provide some sufficient conditions for stabilization with periodic output feedback. The proposed approach is constructive, and for some low dimensional cases, the sufficient conditions that we present are also necessary.
Moreau, L., & Aeyels, D. (2004). Periodic output feedback stabilization of single-input single-output continuous-time systems with odd relative degree. Systems and Control Letters, 51(5), 395-406. https://doi.org/10.1016/j.sysconle.2003.10.001