Structural Properties of Multivariable Linear Systems

摘要

Some parameter-independent structural properties of multivariable linear systems are studied and used to develop analysis and synthesis methods. The structural information is expressed mainly using the controllability and observability Hermite and Kronecker indices. A structured system is defined as a dynamic system where the parameters of its state-space representation are either fixed at zero or independent and non-fixed. It is shown that for structured systems there exist generic lists of Hermite and Kronecker indices, i.e. lists which are actual index lists for almost all non-fixed parameter values. Thus the indices are shown to depend on the structure rather than on the parameter values of the system. New, more general results are found for the relations between the indices and a polynomial matrix representation by introducing the augmented indices to express the information of the uncontrollable and the unobservable modes, too.