Fractional Optimal Control Via Spectral Factorization

The spectral factorization solution for fractional order optimal control problems is provided. First, graphical tools are used to obtain stabilizing controllers as well as derive properties of fractional polynomials. Second, the spectral factorization solution to the output feedback H2 problem is extended to fractional systems, which are permitted to be unstable, non-minimum phase, or incommensurate order. Third, spectral factorization is used to solve the LQR problem of constructing the optimal full-state feedback law, which is shown to have strong connections to the rational LQR