Stabilization of fractional-order singular uncertain systems

The design methods of general state and static output feedback controllers for fractional-order singular (FOS) uncertain linear systems with the order 0<α<1 are proposed.The sufficient conditions for robust asymptotical stability of the FOS closed-loop control systems are presented.The existence conditions and the robust stabilizing controllers are derived by applying matrix׳s singular value decomposition (SVD) and linear matrix inequalities (LMIs) technics.The result of robust asymptotical stabilization is presented in terms of LMIs, which is convenient to the utilized in practice with the help of Matlab LMI Toolbox.

This paper focuses on the state and static output feedback stabilization for fractional-order singular (FOS) uncertain linear systems with the fractional commensurate order 0<α<1, respectively. The objective is to design suitable feedback controllers that guarantee the stability of resulting closed-loop control systems. First, the sufficient conditions for robust asymptotical stability of the closed-loop control systems are presented. Next, based on the matrix׳s singular value decomposition (SVD) and linear matrix inequality (LMI) technics, some new results in the form of LMI are developed to the state and static output feedback controller synthesis for the FOS systems. Finally, three numerical examples are given to illustrate the effectiveness of the proposed design methods.