Robust stabilization of discrete model-reference control systems on integer grid coordinates

This paper describes a robust stabilization problem of discrete model-reference control systems on integer grid coordinates. Currently, all feedback control systems are realized using discretized signals. However, the analysis and design of discrete-time and discrete-value (point-to-point) control systems has not been established. In this paper, the robust stability of that type of discretized control systems is examined in a frequency domain. A robust stability condition for such discrete control systems with multi-nonlinearity is derived by applying Ostrowski´s M-matrix. Using these results, the stabilization and design of model-reference control systems is performed. It can be seen that the model-reference control using a second-order lag system is equivalently transformed into a traditional PID control scheme. Numerical examples for discrete model-reference control are provided to verify the design method.