Robust stabilization criteria of a general form of fractional-order controllers for interval fractional-order plants with complex uncertain parameters

Abstract

This paper studies the problem of robust stabilization of interval fractional-order plants with complex uncertain parameters by using fractional-order controllers. An interval fractional-order plant with complex uncertain parameters means that the coefficients of the numerator and denominator of the plant are all uncertain and may be complex numbers and lie in specified intervals. At first, by using a graphical approach, necessary and sufficient conditions are presented for the stabilization of the fractional-order plant containing complex coefficients. Then, by using some interesting geometric features of convex polygons, a robust stability checking function is presented for the stabilization. Also, an upper frequency bound is introduced to reduce the computational burden. Finally, six examples are provided to illustrate the results.