Hessenberg Input Normal Representations
نویسنده
چکیده
Every stable controllable input pair (Ã , B̃ ) is equivalent to an input pair which is in Hessenberg form and is input normal (AA∗ + BB∗ = I ). (A,B) is represented as a submatrix of the minimal number of Givens rotations. The representation is shown to be generically identifiable. This canonical form allows for fast state vector updates and improved conditioning of system identification problems. EDICS 2-SYSM, 2-IDENT
منابع مشابه
Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
متن کاملGeneralized Bivariate Lucas p-Polynomials and Hessenberg Matrices
In this paper, we give some determinantal and permanental representations of generalized bivariate Lucas p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate Lucas p-polynomials are general forms of, for example, bivariate Jacobsthal-Lucas, bivariate Pell-Lucas ppolynomials, Chebyshev polynomials of the first kind, Jacobsthal...
متن کاملA Multishift Hessenberg Method for Pole Assignment of Single-Input Systems
A new algorithm is proposed for the pole assignment of single-input linear time-invariant systems. The proposed algorithm belongs to the family of Hessenberg methods and is based on an implicit multishift QR-like technique. The new method compares favorably in many respects (speed, memory usage) with existing numerically stable methods. Its improved vectorizability guarantees good opportunities...
متن کاملDeterminantal Representations for Generalized Fibonacci and Tribonacci Numbers
the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Using certain Hessenberg matrices, we provide some determinantal representations of the general terms of second-and third-order linear recurrence sequences with arbitrary initial values. Moreover, we provide explicit formu...
متن کاملOrthonormal Representations for Output System Pairs
A new class of canonical forms is given proposed in which (A,C) is in Hessenberg observer or Schur form and output normal: I − A∗A = C∗C. Here, C is the d × n measurement matrix and A is the advance matrix. The (C,A) stack is expressed as the product of n orthogonal matrices, each of which depends on d parameters. State updates require onlyO(nd) operations and derivatives of the system with res...
متن کامل