Block Companion Matrices, Discrete–time Block Diagonal Stability and Polynomial Matrices
نویسنده
چکیده
A polynomial matrix G(z) = Izm −∑m−1 i=0 Ciz with complex coefficients is called discrete-time stable if its characteristic values (i.e. the zeros of detG(z) ) are in the unit disc. A corresponding block companion matrix C is used to study discrete-time stability of G(z) . The main tool is the construction of block diagonal solutions P of a discrete-time Lyapunov inequality P−C∗PC 0 .
منابع مشابه
ON THE FUNCTION OF BLOCK ANTI DIAGONAL MATRICES AND ITS APPLICATION
The matrix functions appear in several applications in engineering and sciences. The computation of these functions almost involved complicated theory. Thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. The aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. More...
متن کاملNumerical solution of delay differential equations via operational matrices of hybrid of block-pulse functions and Bernstein polynomials
In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...
متن کاملSingly-Bordered Block-Diagonal Form for Minimal Problem Solvers
The Gröbner basis method for solving systems of polynomial equations became very popular in the computer vision community as it helps to find fast and numerically stable solutions to difficult problems. In this paper, we present a method that potentially significantly speeds up Gröbner basis solvers. We show that the elimination template matrices used in these solvers are usually quite sparse a...
متن کاملUpper and lower bounds for numerical radii of block shifts
For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...
متن کاملSome Results on the Field of Values of Matrix Polynomials
In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of ...
متن کامل