Criteria for response monotonicity preserving in approximation of fractional order systems

In approximation of fractional order systems, a significant objective is to preserve the important properties of the original system. The monotonicity of time frequency responses is one of these properties whose preservation is of great importance in approximation process. Considering this importance, the issues of monotonicity preservation of the step response and monotonicity preservation of the magnitude-frequency response are independently investigated in this paper. In these investigations, some conditions on approximating filters of fractional operators are found to guarantee the preservation of step magnitude-frequency response monotonicity in approximation process. These conditions are also simplified in some special cases. In addition, numerical simulation results are presented to show the usefulness of the obtained conditions.