Robust stability conditions of fractional order discrete-time linear systems

Abstract

The paper considers the robust stability problem of uncertain discrete-time fractional order linear state-space systems. The state matrix is the interval matrix whose entries are convex combinations of the entries of two known constant matrices. The necessary and sufficient condition for robust stability is proposed. This condition is stated with respect to eigenvalue-loci placement in the complex plane. The sufficient condition for robust stability based on matrix measures is also given. In this case the rectangle covering all the eigenvalues of the interval state matrix is determined.