Extensions of Kharitonov Theorem to Positive Fractional Linear Systems

Abstract

The asymptotic stability of interval positive continuous-time linear systems of integer and fractional orders is investigated. The classical Kharitonov theorem is extended to the interval positive continuous-time linear systems of integer and fractional orders. It is shown that: (1) The interval positive linear system is asymptotically stable if and only if the matrices bounding the state matrix are Hurwitz Metzler. (2) The interval positive fractional system is asymptotically stable if and only if bounding the state matrix are Hurwitz Metzler. (3) The interval positive of integer and fractional orders continuous-time linear systems with interval characteristic polynomials are asymptotically stable if and only if their lower bounds of the coefficients are positive.