Authors:
Osamu Kaneko,
Takao Fujii,
Volume: 1, Page 1954 Paper number 1898
Abstract:
In this paper, we provide one of the applications of quadratic difference
forms and dissipativeness. By using inherent techniques in discrete
time, we show that the maximum and minimum storage function are described
by almost anti-Hurwitz and Hurwitz spectral factors, respectively,
even if the polynomial matrices have zeros on the unit circle or
singular. Finally, this result is applied to the generalized spectral
factorization problems.
Authors:
Guang-Ren Duan,
Volume: 1, Page 1960 Paper number 1451
Abstract:
Based on a method for right coprime factorizations of linear systems
using matrix elementary transformations, it is shown that a very simple
iteration formula exists for right coprime factorizations of multi-input
linear systems in system upper Hessenberg forms. This formula gives
directly the coefficient matrices of the pair of solutions to the right
coprime factorization of the system Hessenberg form, and involves only
manipulations of inverses of a few triangular matrices and some matrix
productions and summations. Based on this formula, a simple, efficient
procedure for determining a right coprime factorization of a multi-input
linear system is proposed, which first converts a given linear system
into its system Hessenberg form using some orthogonal similarity transformations
and then applies the iteration formula to the converted system Hessenberg
form. An example demonstrates the usage of the approach.
Authors:
Itziar Baragaña,
Victoria Fernández,
Ion Zaballa,
Volume: 1, Page 1966 Paper number 9098
Abstract:
We study the problem of characterizing the Hermite indices of a Linear
System when state feedback is performed. Namely, given the pair (A,
B) we study the problem of the existence of a matrix F such that (A+BF,
B) has prescribed Hermite indices.
Authors:
Konstantin E. Avrachenkov,
Jean B. Lasserre,
Volume: 1, Page 1968 Paper number 1839
Abstract:
We consider an analytic perturbation of the Sylvester matrix equation.
Mainly we are interested in the singular case, that is, when the null
space of the unperturbed Sylvester operator is not trivial, but the
perturbed equation has a unique solution. In this case, the solution
of the perturbed equation can be given in terms of a Laurent series.
Here we provide a necessary and sufficient condition for the existence
of a Laurent series with a first order pole. An efficient recursive
procedure for the calculation of the Laurent series' coefficients is
given. Finally, we show that in the particular, but practically important
case of semisimple eigenvalues, the recursive procedure can be written
in a compact matrix form.
Authors:
Itziar Baragaña,
Victoria Fernández,
Ion Zaballa,
Volume: 1, Page 1974 Paper number 7
Abstract:
The problem of the existence of Linear Systems with prescribed structural
invariants for system similarity is studied. Namely, we solve the problem
of the existence of such a system with prescribed controllability indices,
Hermite indices and invariant factors when the invariant factors of
A (which are also invariants under system similarity) are given.
Authors:
Xinmin Liu,
Ben M. Chen,
Zongli Lin,
Volume: 1, Page 1979 Paper number 1171
Abstract:
A systematic method is developed for determining an output matrix C
for a given matrix pair (A,B) such that the resulting linear system
characterized by the matrix triple (A,B,C) has the pre-specified system
structural properties, such as the finite and infinite zero structure
and the invertibility structures. Since the matrix C describes the
locations of the sensors, the procedure of choosing C is often referred
to as sensor selection. The method developed in this paper for sensor
selection can be applied to the dual problem of actuator selection,
where, for a given matrix pair (A,C), a matrix B is to be determined
such that the resulting matrix triple (A,B,C) has the pre-specified
structural properties.
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