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# Accession Number:

## ADA151491

# Title:

## The Matrix Sector Functions and their Applications to Systems Theory.

# Descriptive Note:

## Rept. for 1 Jul-31 Dec 84,

# Corporate Author:

## HOUSTON UNIV TX DEPT OF ELECTRICAL ENGINEERING

# Report Date:

## 1984-09-01

# Pagination or Media Count:

##
12.0

# Abstract:

## The paper presents a new matrix function, the matrix sector function of a square complex matrix A, and its applications to systems theory. Firstly, based on an irrational function of a complex variable, a scalar sector function is defined. Next, a fast algorithm is developed with the help of a circulant matrix for computing the scalar sector function of lambda. Then, the scaler sector function of lambda is extended to a matrix sector function, and to associated partitioned matrix sector functions of A. Finally, the applications of these matrix sector functions to the separation of matrix eigenvalues, the determination of A-invariant space, the block diagonalisation of a matrix, and the generalised block partial fraction expansion of a rational matrix are given. It is shown that the well-known matrix sign function of A is a special class of the newly developed matrix sector function of A. It is also shown that the Newton-Raphson type algorithm cannot, in general, be applied to determine the matrix sector function of A. Originator supplied keywords include Mathematical technique Approximation theory Eigenfunctions Linear systems.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#