Supplemental Stability Criteria with New Formulation for Linear Time-Invariant Fractional-Order Systems

Abstract

In this paper, new stability criteria for linear time-invariant fractional-order systems (LTIFOSs) based on linear matrix inequalities (LMIs) are derived. The solved variable of the existing LMI formulations is generalized to a complex one. In addition, based on the congruent transformation, a new LMI formulation is obtained, which is different from those in the existing literature. To deal with the above LMIs more conveniently with simulation software, the complex LMIs are converted to equivalent real LMIs. Finally, numerical examples are presented to validate the effectiveness of our theoretical results.

Keywords

• fractional-order systems
• Kronecker product operator
• congruent transformation
• linear matrix inequality