Guaranteed cost control for uncertain fractional order LTI systems

Abstract

This brief addresses a guaranteed cost control problem for norm-bounded parameter uncertain fractional order systems with order $\alpha$ between 0 and 1. It is meaningful both in theory and application. Using the stability theorem of fractional order LTI systems, a sufficient condition of the design of state feedback controller is provided that ensure the stability problem of closed-loop system with less than an upper bound for all parameter uncertainties of a specified quadratic cost performance index. All the results are expressed in terms of linear matrix inequalities without equality constraint and the criterion is a special case of integer order systems. Finally, the effects and the applicability of our results are illustrated via a numerical simulational example and a practical example.