Quadratic Admissibility for a Class of LTI Uncertain Singular Fractional-Order Systems with 0 < α < 2

Abstract

This paper provides a unified framework for the admissibility of a class of singular fractional-order systems with a given fractional order in the interval (0, 2). These necessary and sufficient conditions are derived in terms of linear matrix inequalities (LMIs). The considered fractional orders range from 0 to 2 without separating the ranges into (0, 1) and [1, 2) to discuss the admissibility. Moreover, the uncertain system with the fractional order in the interval (0, 2) is norm-bounded. The quadratic admissibility and general quadratic stability of the system are analyzed, and the equivalence between the two is proved. All the above can be expressed in terms of strict LMIs to avoid any singularity problem in the solution. Finally, the effectiveness of the method is illustrated by three numerical examples.