PLACING ZEROES and the KRONECKER CANONICAL FORM
نویسندگان
چکیده
Given a linear time-invariant control system, it is well known that the transmission zeroes are the generalized eigenvalues of a matrix pencil. Adding outputs to place additional zeroes is equivalent to appending rows to this pencil to place new generalized eigenvalues. Adding inputs is likewise equivalent to appending columns. Since both problems are dual to each other, we only show in this paper how to choose the new rows to place the new zeroes in any desired locations. The process involves the extraction of the individual right Kronecker blocks of the pencil, accomplished entirely with unitary transformations. In particular, when adding one new output, i.e. appending a single row, the maximum number of new zeroes that can be placed is exactly the largest right Kronecker index.
منابع مشابه
The Quasi-Kronecker Form For Matrix Pencils
We study singular matrix pencils and show that the so called Wong sequences yield a quasi-Kronecker form. This form decouples the matrix pencil into an underdetermined part, a regular part and an overdetermined part. This decoupling is sufficient to fully characterize the solution behaviour of the differential-algebraic equations associated with the matrix pencil. Furthermore, the Kronecker can...
متن کاملInterconnection of Kronecker canonical form and special coordinate basis of multivariable linear systems
This paper establishes a straightforward interconnection between the Kronecker canonical form and the special coordinate basis of linear systems. Such an interconnection yields an alternative approach for computing the Kronecker canonical form, and as a by-product, the Smith form, of the system matrix of general multivariable time-invariant linear systems. The overall procedure involves the tra...
متن کاملOn the Stratiication of the Kronecker Canonical Form
The understanding of which Kronecker structures that are close to a given structure is revealed by the Kronecker structure hierarchy, i.e., the strati cation of the Kronecker canonical form. For a given matrix pencil A B, the Kronecker structure hierarchy shows all structures that are within the closure of orbit(A B), and each structure, whose orbit's closure contains A B. In order to gain new ...
متن کاملInterconnection of the Kronecker Form and Special Coordinate Basis of General Multivariable Linear Systems
This paper establishes a straightforward interconnection between the Kronecker canonical form and the special coordinate basis of linear systems. Such an interconnection enables the computation of the Kronecker canonical form, and as a by-product, the Smith form, of the system matrix of general multivariable time-invariant linear systems. The overall procedure involves the transformation of a g...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS On Kronecker Canonical Form of Mixed Matrix Pencils
A mixed matrix pencil is a matrix pencil which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. In this paper, we characterize the indices of nilpotency of the Kronecker canonical form for a mixed matrix pencil in terms of matroids. As a byproduct, we provide an algorithm for computing t...
متن کامل