Discretized model-reference feedback and robust stabilization for continuous plants on integer grid coordinates

This paper deals with a robust stabilization problem of discrete model-reference control systems on integer grid coordinates. At present, 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 modelreference control using a second-order lag system is equivalently transformed into a traditional PID control scheme. Numerical examples including a controlled system with time delay are provided to verify the design method.