Simultaneous estimation of system states and identification of time-varying parameters for discrete-time systems via iterative learning estimation

In this paper, the state estimation problem and identifying time-varying parameters are investigated for discrete-time systems with time delays. The time delays comprise both state delay and measurement delay. A novel iterative learning estimator, which is utilized to eliminate the effects of state delay and measurement delay is presented for the general systems. The main idea on the design of the iterative learning estimator is to combine the previous information into the proposed estimator for identifying time-varying parameters in real time by the use of learning. The sufficient conditions for the solvability of the addressed problem are obtained in terms of certain linear matrix inequalities(LMIs). An explicit expression of the desired iterative learning estimator is also given. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.