Security and vulnerability in the stabilization of networks of controlled dynamical systems via robustness framework

This paper addresses the issues of security and vulnerability of links in the stabilization of networked control systems from robustness viewpoint. As is done in recent research, we view network security as a robustness issue. However, in this paper we shed considerable new insight into this topic and offer a new and differing perspective. We argue that `robustness' aspect is a common theme related to both vulnerability and security. This paper puts forth the viewpoint that vulnerability of a networked system is a manifestation of the combination of two types of robustness, namely `qualitative robustness' and `quantitative robustness'. In other words, the entire robustness concept is treated as a combination of qualitative robustness and quantitative robustness, wherein qualitative robustness is linked to the system's nature of interactions and interconnections i.e. system's structure while quantitative robustness is linked to the system dynamics. Put it another way, qualitative robustness is independent of magnitudes and depends only on the signs of the system dynamics matrix whereas quantitative robustness is purely a function of the quantitative information (both magnitudes and signs) of the entries of the system dynamics matrix. In that sense, these two concepts are inter-related, each influencing and complementing the other. Applying these notions to the networked control systems represented by `dynamical structure functions', it is shown that any specific dynamical structure function originated by a state space represenation, is a function of both qualitative and quantitative robustness. In other words, vulnerability of links in that network is determined by both the signs and magnitudes of that state space matrix of that dynamical structure function. Thus the notion in the recent literature that `vulnerability depends on the system structure, not the dynamics and the robustness, which depends on the dynamics, and not on the system structure' is disputed and clear justification for our viewpoint is provided by newly introduced notions of `qualitative robustness' and `quantitative robustness'. This paper then presents few specific dynamical structure functions that possess a large number of non-vulnerable links which is desirable for a secure network. The proposed concepts are illustrated with many useful examples.