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 ...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.展开更多
Dear Editor,The distribution of eigenvalues,i.e.,the zeros of the characteristic functions of linear time-invariant(LTI)systems,is of great significance for analyzing and synthesizing the performance of these systems....Dear Editor,The distribution of eigenvalues,i.e.,the zeros of the characteristic functions of linear time-invariant(LTI)systems,is of great significance for analyzing and synthesizing the performance of these systems.The research on the distribution of eigenvalues mainly focuses on the determination of the number of zeros of polynomials or quasipolynomials in a fixed region of the entire complex plane,where the determination of the distribution of zeros of quasi-polynomials has always been a challenging issue[1],[2].Recently,several results on the determination of the number of zeros of a class of quasi-polynomials in the open right-half complex plane were derived in[3],where the quasi-polynomials can be neutral type with complex(real)coefficients.展开更多
基金supported by the National Natural Science Foundation of China (60572093)the Natural Science Foundation of Beijing(4102050)
文摘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.
基金supported by the National Natural Science Foundation of China(NSFC)(62473085 and 61703086)the IAPI Fundamental Research Funds(2018ZCX27)
文摘Dear Editor,The distribution of eigenvalues,i.e.,the zeros of the characteristic functions of linear time-invariant(LTI)systems,is of great significance for analyzing and synthesizing the performance of these systems.The research on the distribution of eigenvalues mainly focuses on the determination of the number of zeros of polynomials or quasipolynomials in a fixed region of the entire complex plane,where the determination of the distribution of zeros of quasi-polynomials has always been a challenging issue[1],[2].Recently,several results on the determination of the number of zeros of a class of quasi-polynomials in the open right-half complex plane were derived in[3],where the quasi-polynomials can be neutral type with complex(real)coefficients.
