In this work is proposing fractional controller realized by rational approximation of irrational function. The aim of this paper is to systemize some methods for discrete ap-proximation using numerical integration and power series expansion (PSE), discrete approximation using numerical integration and continued fraction expression (CFE). An example of realization of the particular case of digital fractional order controller is shown with PIC microprocessor and realized discrete approximation by continued fraction ex-pression of Al-Alaoui operator.

The paper presents a proof for the applicability of a method for synthesis of robust internal model control systems. The case of discrete-time systems synthesis is discussed.