Discrete Interval Systems Research Articles

Counter-example to 'Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems'

Abstract In this note, the interval matrix result for discrete linear interval system by Jiang (1988) is shown to be incorrect, i.e. all eigenvalues of each matrix A ε A 1 (an interval matrix) have magnitudes less than 1 if and only if all the eigenvalues of every ‘extreme matrix’ of the interval matrix A 1 have magnitudes less than 1.

Comments on 'Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems'

Comments on 'Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems'

Comments on 'Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems'

Abstract In a recent paper by Jiang (1988), a necessary and sufficient condition for asymptotic stability of the interval matrix of discrete-time systems is presented. In this contribution it is shown that this condition is not true in general. A counter-example is given and additional remarks are made.

Comments on ‘Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems’

In a recent paper by Jiang (1988), a necessary and sufficient condition is given for a set of real interval matrices to have all their eigenvalues in the unit circle. This result is shown by counter-example to be false and the flaw in the proof is pointed out.

Counter-examples to ‘Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems’

Jiang (1988) gives a sufficient and necessary condition for the asymptotic stability of a discrete linear interval system. It is here demonstrated through counter-examples that the condition is not sufficient. The flaw leading to this erroneous result is also indicated.

Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems

In this paper, a sufficient and necessary condition for the asymptotic stability of the discrete linear interval system X(k + 1) = A1X(k) is presented; i.e. all the eigenvalues of each matrix AϵA1, (an interval matrix) have magnitudes less than 1 if and only if all the eigenvalues of every ‘extreme matrix’ of the interval matrix A1, have magnitudes less than 1.