Controllability and reducibility conditions of a new system model

Abstract

A new system model (a class of RFSs) (A, B) is proposed, where A=(G+D)-1C and B are, respectively, an n×n and an n×m matrix over the field F(ξ, z); D and C are two matrices over F(z), F(z) denotes the field of all rational functions in q independently variable parameters z1, …, zq, z=(z1,…,zq) q≥0; G=diag(0, G22), G22=diag(ξ1,…, ξn2), n2≤n, ξ=(ξ1,…,ξ2); F(ξ, z) is the field of all rational functions in q+n2 mutually independent parameters ξ1,…,ξn2, z1,…,zq. The model can describe most linear physical systems such as electrical networks and servo systems. The controllability condition of the system (A, B) and the reducibility condition of the nonzero part of the polynomial det(λI-A) are derived. An illustrative example is given.