Design and analysis of linear equality constrained dynamic systems

The state of many dynamic systems evolves subject to some equality constraints. Under the assumption that the equality constrained dynamic systems are already available, most existing work focuses on developing state estimation algorithms for these systems. However, how to design and analyze such a system is rarely addressed, even though it is critically important for performance evaluation and application. In this paper, unlike the existing system conversion-based design techniques, we propose a new systematic way to design and analyze linear equality constrained linear dynamic systems through a direct elimination technique, where the desired model class is given and only the distributions of the initial state and driving process noise need to be determined. Comparatively, it is much easier. It is also found that the existing formulations of linear equality constrained linear dynamic systems only cover a small part of the whole class. Numerical examples are provided to illustrate the effectiveness of the proposed way of design and analysis.