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It is difficult to determine the stability of linear systems with interval delays (LID systems) because the roots of the characteristic polynomials of the systems are continuous and vary in a complex plane with the delay. To solve the problem, this paper develops a stability test of LID systems by resorting to 2-D hybrid polynomials and 2-D Hurwitz-Schur stability. Comparing with the existing test approaches for LID systems, the proposed 2-D Hurwitz-Schur stability test is easy to apply, and can obtain closed form constraint conditions for system parameters. This paper proposes some theorems as sufficient conditions for the stability of LID systems, and also reveals that recent results about the stability test of linear systems with any delays (LAD systems) are not suitable for LID systems because they are very conservative for the stability of LID systems.
It is difficult to determine the stability of linear systems with interval delays (LID systems) because the roots of the characteristic polynomials of the systems are continuous and vary in a complex plane with the delay. To solve the problem, this paper develops a stability test of LID systems by resorting to 2-D hybrid polynomials and 2-D Hurwitz-Schur stability. Comparing with the existing test approaches for LID systems, the proposed 2-D Hurwitz-Schur stability test is easy to apply, and can obtain closed form constraint conditions for system parameters. This paper proposes some theorems as sufficient conditions for the stability of LID systems, and also reveals that recent results about the stability test of linear systems with any delays (LAD systems) are not suitable for LID systems because they are very conservative for the stability of LID systems.