Schur Stability Of Interval Matrices Research Articles

Note on Schur stability of three‐dimensional interval matrices

SummaryWell‐known results on robust Hurwitz and Schur stability of interval polynomials and interval matrices are discussed. We fill in some gap in this theory. It is proved that, for , Schur stability of vertex matrices is not sufficient for robust Schur stability of the interval matrix. A certain general method for constructing examples of this kind is presented.

Improved bounds for the spectrum of interval matrices

This study presents new sufficient conditions for Hurwitz and Schur stability of interval matrices. Tight bounds for the spectrum of interval matrices are estimated using computationally simple optimisation problems. The conservativeness is reduced further by application of ordinary similarity transformation. A necessary and sufficient vertex based criterion for the stability of a subclass of interval systems in continuous and discrete-time cases is also proposed. This enables the spectra for this class of interval systems to be determined exactly. A selection of various examples adopted from existing literature is used to demonstrate the utility of the proposed criteria.

On the stability of a family of nonlinear time-varying systems

In the present paper we investigate several types of Lyapunov stability of an equilibrium x/sub e/ of a family of finite dimensional dynamical systems determined by ordinary differential (difference) equations. By utilizing the extreme systems of the family of systems, we establish sufficient conditions, as well as necessary conditions (converse theorems) for several robust stability types. Our results enable us to realize a significant reduction in the computational complexity of the algorithm of Brayton and Tong (1979) in the construction of computer generated Lyapunov functions. Furthermore, we demonstrate the applicability of the present results by analyzing robust stability properties of equilibria for Hopfield neural networks and by analyzing the Hurwitz and Schur stability of interval matrices.

Comments regarding "On stability of interval matrices" [with reply

We note that several of the results on Schur-stability of interval matrices in the above paper by Sezer-Siljak (ibid. vol.39) can be viewed as special cases of results obtained in a more general framework, and some of the latter were previously reported in the literature. In reply, Sezer-Siljak response to the issues raised in the comment.

Comments on "Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices"

This note shows that example 1 in the above paper by Wang et al. (see ibid., vol.39, p.1250-55, 1994) is not Hurwitz stable.

Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices

Establishes a set of new sufficient conditions for the Hurwitz and Schur stability of interval matrices. The authors use these results to establish necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices. The authors relate the above results to the existence of quadratic Lyapunov functions for linear time-invariant systems with interval-valued coefficient matrices. Using the above results, the authors develop an algorithm to determine the Hurwitz and the Schur stability properties of interval matrices. The authors demonstrate the applicability of their results by means of two specific examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Positive Definiteness and Stability of Interval Matrices

Characterizations of positive definiteness, positive semidefiniteness, and Hurwitz and Schur stability of interval matrices are given. First it is shown that an interval matrix has some of the four properties if and only if this is true for a finite subset of explicitly described matrices, and some previous results of this type are improved. Second it is proved that a symmetric interval matrix is positive definite (Hurwitz stable, Schur stable) if and only if it contains at least one symmetric matrix with the respective property and is nonsingular (for Schur stability, two interval matrices are to be nonsingular). As a consequence, verifiable sufficient conditions are obtained for positive definiteness and Hurwitz and Schur stability of symmetric interval matrices.

On sufficient conditions for the stability of interval matrices

We investigate the Hurwitz and Schur stability of interval matrices using Lyapunov's second method and interval analysis techniques. Previous results require a check of the definiteness of 2 n(n − 1)/2 concerns of a certain interval matrix. The present results require a check of the definiteness of only 2 n − 1 corners.

Counter-example to a recent result on the Schur stability of interval matrices by C.-l. Jiang

Abstract Jiang (1988) stated that the Schur stability of an interval matrix A I is equivalent to that of the vertices of A I . We point out, via a counter-example, that this result is incorrect.

Counter-example to a recent result on the Schur stability of interval matrices by C.-I. Jiang

Counter-example to a recent result on the Schur stability of interval matrices by C.-I. Jiang