Stability and Performance Attainment with Fixed Order Controller Using Frequency Response

Recently, a new data driven controller synthesis is presented for calculating the family of stabilizing first, second and fixed order controller using frequency respons. However, this method is applicable just for plants that can guarantee some smoothness at the boundary of the resulted high dimension LMI. This paper solve that issue and extends the approach to fixed order controllers guaranteeing some performance criteria which are applicable for the more general types of plants. It is shown that knowing the frequency response of plant is sufficient to calculate the stabilizing fixed order controllers from a set of convex linear inequalities. The norm on sensitivity and complementary sensitivity functions are satisfied from some frequency domain inequalities (FDI) that could be examined from frequency response data. The usefulness of the proposed approach is illustrated by an academic example.