Adaptive control with delta operator based on gradient method

In high sampling systems, with the increase of sampling frequency, discrete time systems design based on conventional shift operator will push all the poles to edge of the unit circle, therefore causes the instability of the discrete time system model, and hence can not proceed with the controller design. Discrete system design based on Delta operator can avoid this problem and achieve better results. This paper utilizes gradient method to design adaptive system based on Delta Operation model and better result can be seen by comparing with system based on Z conversion under high speed sampling system.