New sufficient conditions for the stability of continuous and discrete time-delay interval systems

Abstract Based on the Gersgorin theorem, this paper discusses the stability testing problem for continuous and discrete interval systems including a time delay. Several new delay-independent sufficient conditions for preserving the stability of the above systems are developed. By these conditions, criteria that can guarantee the mentioned systems be stable with a decaying rate are also proposed. Finally, numerical examples are given to demonstrate the applicability of the obtained results.

[1]  Wei-Bin Gao,et al.  STABILITY OF INTERVAL PARAMETER MATRICES , 1987 .

[2]  M. Argoun.  Near-decoupling of linear multivariable systems , 1986 .

[3]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[4]  S. Bialas,et al.  Necessary and Sufficient Conditions for the Stability of Interval Matrices , 1983 .

[5]  C. Jiang.  Sufficient condition for the asymptotic stability of interval matrices , 1987 .

[6]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[7]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[8]  Hiroyuki Tamura,et al.  A Discrete Dynamic Model with Distributed Transport Delays and Its Hierarchical Optimization for Preserving Stream Quality , 1974, IEEE Trans. Syst. Man Cybern..

[9]  Yau-Tarng Juang,et al.  Stability analysis of dynamic interval systems , 1989 .

[10]  M. Argoun.  Allowable coefficient perturbations with preserved stability of a Hurwitz polynomial , 1986 .

[11]  Madan G. Singh,et al.  Modelling and hierarchical optimization for oversaturated urban road traffic networks , 1974 .

[12]  Robin J. Evans,et al.  Stability analysis of interval matrices―continuous and discrete systems , 1988 .

[13]  Djordjija B. Petkovski.  Stability analysis of interval matrices: improved bounds , 1988 .

[14]  W. Karl,et al.  Comments on ‘ A necessary and sufficient condition for the stability of interval matrices ’† , 1984 .

[15]  Sheng-De Wang,et al.  Root-locus approach to the stability analysis of interval matrices , 1987 .

[16]  H. Tamura.  Decentralized optimization for distributed-lag models of discrete systems , 1975, Autom..

[17]  Y. Shi.  Comments on ‘Stability of an entire polytope of polynomials’ , 1990 .

[18]  Rama K. Yedavalli.  Stability analysis of interval matrices: another sufficient condition , 1986 .

[19]  C. B. Soh,et al.  Stability margins of continuous time interval systems , 1991 .

[20]  Improved robust performance bounds in covariance majorant analysis , 1989 .

[21]  E. I. Jury,et al.  Robust Schur-stability of control systems with interval plants , 1990 .

[22]  C. Soh.  Necessary and sufficient conditions for stability of symmetric interval matrices , 1990 .

[23]  Sufficient condition for the positive definiteness of symmetric interval matrices , 1991 .