Discretization of linear continuous systems with input output time delay

The presence of delays makes system analysis and control design much more complicated. Delays deteriorate the control performance and could destabilize the overall system in the theory of discrete-time signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control applications, the data as seen from the computer and systems involved are naturally discrete-time because a computer executes program code at discrete points of time. In this paper, a new approximated discretization method and digital design for control systems with delays is proposed. System is transformed to a discrete-time model with time delays. To implement the digital modeling, we used the z-transfer functions matrix. The z-transform of discrete-time signals plays much the same role as the Laplace transform for continuous-time systems. The most important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended discrete-time, using an integral numerical approximation, typically Euler´s forward method, Euler´s backward method or Tustin´s method. Illustrative example is simulated to demonstrate the effectiveness of the developed method.