Further Results on Structural Assignment of Linear Systems

This paper considers the problem of assigning structural properties of a linear system through sensor selection. The problem is, for a given matrix pair (A,B), to find an output matrix pair (C,D) such that the resulting linear system (A,B,C,D) has the pre-specified structural properties, such as the finite and infinite zero structures and the invertibility properties. Both the assignability of certain structural properties is established and an algorithm for explicitly constructing the matrices (C,D) that result in these properties is developed. In particular, by introducing the notion of infinite zero assignable sets for the pair (A,B), we establish necessary conditions under which a given set of structural properties can be assigned. Motivated by these necessary conditions, we establish a set of necessary and sufficient conditions for the assignability of a set of structural properties which includes left invertibility property. These necessary and sufficient conditions indicate the conservativeness of the existing conditions. In establishing these conditions, we develop a numerical algorithm for the construction of the required output matrix pair (C,D).