Finite-time settling adaptive observer for linear discrete-time systems

This paper deals with a design method for an adaptive scheme which would identify the parameters and observe the state of any unknown single-input single-output linear discrete-time systems using only input-output data. Kreisselmeier's parametrized system [5] is used instead of the original system. Then the parameter identification process and the state observation process are well separated. To accelerate the convergence rate of the estimates, a finite-time settling scheme is proposed. It is shown that the estimates obtained converges to true values at k = 3n ?1, where k is the discrete time and n is the order of system. A numerical example is given to indicate acceptable performance of the proposed scheme.