Algebraic systems theory toward stabilization under parametrical and degree changes in the polynomial matrices of linear mathematical models

Abstract

This paper deals with the stabilization of the linear time-invariant finite dimensional control problem specified by the following linear spaces and subspaces on C: ? (state space) = ?* Å ?d, U (input space) = U1 Å U2, Y (output space) = Y1 + Y2, together with the linear mappings: Qs = ? x U x [0,t} --> ? associated with the evolution equation of the C0-semigroup S(t) generated by the matrices, of real and complex entries A belonging to L(?,?) and B belonging to L(U,?) of a given differential system. The stabilization for variations in the values of the parameters and structures of the above matrices with respect to a nominal system (of state space ?*) is investigated. The study is made in the context of algebraic systems theory and it includes the variation of the degrees, but not of the orders, of the associated polynomial matrices with respect to the nominal ones.