Algebraic characterization of arbitrary pole assignability by static output feedback”“

Abstract

Based on the explicit algebraic dependences p — g(F) between the vector p of the closed-loop characteristic-polynomial coefficients and the static output feedback matrix F, the well-known problem of arbitrary pole assignability by static output feedback is considered: local pole assignability is possible if and only if the differential g* has full rank. Taking advantage of the known analytical dependences of g*FF on F, new sufficient criteria for global pole assignability are derived. An explicit formula to compute the algebraic submanifold of feedback matrices F for which g*F does not have full rank is also obtained. If the property of local pole assignability holds, then there exists a smooth submanifold of matrices F each point of which ensures the desired pole assignment. An algorithm by which this smooth submanifold can be computed is outlined. Illustrative examples are discussed in some detail.