Development of robust analysis tools and interface programs for fractional order uncertain systems

In this thesis, analysis methods and interface programs are presented for fractional order uncertain polynomials and transfer functions. Stability analysis of polynomials with linear and nonlinear uncertainty structures are performed using value set analysis and zero exclusion principle. 2q-convex parpolygon approach is presented for computational convenience in the analysis of fractional order polynomials with linear uncertainties. Bode and Nyquist envelopes of fractional order uncertain systems are computed with the aid of 2q-convex parpolygon approach. Analysis of polynomials and systems with multiple linear uncertainty are performed by value set and zero exclusion principle. Then, Bode and Nyquist envelopes of such systems are obtained. Procedure to obtain Bode and Nyquist boundaries which include Bode and Nyquist plots of systems with nonlinear uncertainty structures is given and Lag-Lead compensator is designed for such systems. An analysis method for fractional order systems with unstructured uncertainty models is proposed. Roots region analysis, as another method that could be used for stabilty analysis of fractional order polynomials is presented and roots regions of fractional order polynomials with single and multiple uncertainty structures are computed. Hermite-Biehler theorem, which is a useful method for classical polynomials, is generalized for fractional order polynomials and its efficiency is shown on examples. Then, an interface is designed and presented for easy usage of methods for robust stability analysis of fractional order polynomials and systems. Therefore, a program for researchers who deal with fractional order systems is gained to the literature.