Robust stability and stabilization of fractional-order systems with polytopic uncertainties via homogeneous polynomial parameter-dependent matrix forms

Abstract

This paper addresses the robust stability and stabilization problems for fractional-order systems with polytopic uncertainties. By introducing homogeneous polynomial parameter-dependent matrix forms, the robust stability and stabilization conditions can be expressed as square matricial representation (SMR) of matrix forms, which is finally reduced to solving linear matrix inequalities (LMIs). Since the auxiliary matrices are all homogeneous polynomial parameter-dependent, the proposed method is effective and less conservative than the existing results, which is illustrated by the final numerical examples.