Admissibility LMI criteria for descriptor fractional-order systems with a changeable number of decision variables

Abstract

This paper studies the admissibility problem of descriptor fractional-order systems (DFOSs) with order in (0,1). Firstly, an approach to stability for FOSs is derived which is effective for the case of at least two complex matrix variables. Secondly, based on the generalized linear matrix inequality (GLMI) region, a new admissibility criterion for DFOSs with multiple choices for the number of decision variables is presented, which does not involve complex variables and equality constraints. Moreover, all the theorems are necessary and sufficient conditions, and can be described by strict linear matrix inequalities (LMIs). Finally, two numerical examples are provided to verify the validity of theoretical conclusions.