Projective state observers for large-scale linear systems

In this paper, towards efficient state estimation for large-scale linear systems, we propose a novel framework of low-dimensional functional state observers, which we call a projective state observer, with the provision of a systematic design procedure. The projective state observer can be regarded as a generalization of functional state observers that is defined by means of the orthogonal projection taking into account the system controllability/observability in a quantitative manner. The efficiency of the proposed observer is shown through a numerical example for a reaction-diffusion system evolving over a directed complex network. Moreover, through this observer design, we discuss a trade-off relation between low-dimensionality and an observation error.