New sufficient criteria for Schur D‐stability of interval matrices

Abstract

Purpose

The purpose of this paper is to discuss the Schur D‐stability and the vertex stability of interval matrices (including point matrix obviously). Some new sufficient conditions (criteria) are proposed which guarantee the interval matrix is Schur D‐stable. This results are shown to be less conservative than those in recent literatures. In addition, two equivalence relations between the Schur D‐stability and the vertex stability of interval matrices will be proposed and a new Schur D‐stability range of an interval matrix presented.

Design/methodology/approach

Matrix eigenvalues theory and matrix measure approach.

Findings

Several simple sufficient conditions (criteria) for guaranteeing the Schur D‐stability of interval matrices are derived, two equivalence relations between the Schur D‐stability and the vertex stability of interval matrices are proposed, and a new Schur D‐stability range of an interval matrix is presented.

Research limitations/implications

Control theory or stability theory. These stability criterion possess simple forms and provide useful tools to check Schur D‐stability of interval matrices (including point matrix) at first stage.

Practical implications

The paper provides useful tools to check Schur D‐stability of interval matrices (including point matrix) at first stage.

Originality/value

Two equivalence relations between the Schur D‐stability and the vertex stability for general interval matrices (including point matrix) are proposed, such that the conditional limitations for tridiagonal matrix in recent papers are broken. A new Schur D‐stability range of an interval matrix is presented, and several simple sufficient conditions are obtained which guarantee the Schur D‐stability of interval matrices (including point matrix).

Citation

Shi, G., Han, J., Gao, J. and Wang, Q. (2009), "New sufficient criteria for Schur D‐stability of interval matrices", Kybernetes, Vol. 38 No. 3/4, pp. 474-480. https://doi.org/10.1108/03684920910944182