Frequency boundary of fractional order systems with nonlinear uncertainties

This paper proposes a method to compute frequency boundaries of fractional order control systems with nonlinear uncertainty structures that include and guarantee the Bode and Nyquist envelopes. Then, a lag-lead compensator is designed based on the frequency boundary to provide desired gain and phase specifications. Two types of nonlinear uncertainty structures, namely polynomial and general uncertainties, have been concerned in illustrative examples to explain computing process clearly.