A Graph Separation Stability Condition for Non-Planar Conic Systems

Results related to an extension of the notion of nonlinear conic systems to the non-planar case are presented. Specifically, parametrization of the non-planar dynamic conic sectors in terms of their central subspace and radius is developed. Relationship between (Q,S,R)-dissipativity and non-planar conicity is studied; in particular, it is shown that any (Q,S,R)-dissipative system is non-planar conic, and a procedure for calculation of the central subspace and the radius is presented. A graph separation stability condition for interconnections of non-planar conic systems is formulated and proven. The results presented in this work will form a background for the future extensions of the scattering transformation-based stabilization techniques to the case of interconnections of non-planar conic systems. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.