Completeness on the stability criterion of fractional order LTI systems

Abstract

AbstractThe importance of the concept of stability in fractional order system and control has been recognized for some time now. Recently, it has become evident that many conclusions were drawn, but little consensus was reached. Consequently, there is an urgent need for a much deeper understanding of such a concept. With the definition of fractional order positive definite matrix, a set of equivalent and elegant stability criteria are developed via revisiting a stability criterion we proposed before. All the results are formed in terms of linear matrix inequalities. Afterwards, a series of interesting properties of these criteria are revealed profoundly, including completeness, singularity, conservatism, etc. Eventually, a simulation study is provided to validate the effectiveness of the obtained results.