On the Stability Bounds of Kalman Filters for Linear Deterministic Discrete-Time Systems

In this article, we prove input-to-state stability of the estimation error of the discrete-time Kalman filter under suitable assumptions. Input-to-state stability is an important prerequisite for the use of many contemporary analysis tools for cascaded and interconnected systems. In this way, this article provides a missing link for the rigorous analysis of systems, of which the Kalman filter is a subsystem, using these tools.