Analysis of Control Systems on Symmetric Cones
It is well known that exploiting special structure is a powerful way to extend the reach of current optimization tools to higher dimensions. While many linear control systems can be treated satisfactorily with linear matrix inequalities (LMI) and semidefinite programming (SDP), practical considerations can still restrict scalability of general methods. Thus, we wish to work with high dimensional systems without explicitly forming SDPs. To that end, we exploit a particular kind of structure in the dynamics matrix, paving the way for a more efficient treatment of a certain class of linear systems. We show how second order cone programming (SOCP) can be used instead of SDP to find Lyapunov functions that certify stability. This framework reduces to a famous linear program (LP) when the system is internally positive, and to a semidefinite program (SDP) when the system has no special structure.
© 2015 IEEE. We thank S. You, N. Matni, and A. Swaminathan for helpful discussions. This work was supported in part by a Department of Defense NDSEG Fellowship, Terraswarm, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA, and by the Boeing company.
Submitted - jordan_cdc2015.pdf