Negativizability: A useful property for distributed state estimation and control in Cyber–Physical Systems

In this paper we focus our attention on an interesting property of linear and time-invariant systems, namely negativizability: a pair (A,C) is negativizable if a gain matrix K exists such that A−KC is negative definite. Notably, in this paper we show that negativizability can be a useful feature for solving distributed estimation and control problems in Cyber–Physical Systems (CPS), since such a property allows a network of agents to bring the estimation error to zero or to control the overall system by designing gains that only require information locally available to each agent. In detail, we first characterize the negativizability problem, developing a necessary and sufficient condition for the problem to admit a solution. Then, we show how distributed estimation and control schemes for linear and time-invariant CPSs can greatly benefit from this property. A simulation campaign aiming at showing the potential of negativizability in the context of distributed state estimation and control of CPSs concludes the paper.