A Kalman-type observer for discrete-time systems with multiple delays

In this note a useful and systematic approach to design observers for discrete-time systems with multiple delays, under general conditions, is presented. The proposed technique is developed along the lines of the Kalman filter while the observer´s order is independent from the number of delays and, is equal to the state dimension. From the comparison to the global Kalman algorithm, it is shown that under the observability condition asymptotic convergence is guaranteed. To illustrate properties of the proposed observer, a numerical example is provided