In this paper,the authors discuss the measure of interval matrices and its applications.The authors give a new method of the stability of interval matrices and get some sufficient and neessary conditions for it.These ...In this paper,the authors discuss the measure of interval matrices and its applications.The authors give a new method of the stability of interval matrices and get some sufficient and neessary conditions for it.These results are contained in work [4-9].展开更多
Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and exten...Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.展开更多
For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij<...For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij</sub>},（1）B=(b<sub>ij</sub>)<sub>n×n</sub>=B<sup>T</sup>,C=(c<sub>ij</sub>)<sub>n×n</sub>=C<sup>T</sup>∈R<sup>n×n</sup>,Bialas has studied the necessary and sufficient condi-tion of asymptotic stabilty of G[B,C].According to refs[2-6],the following result,the asympotic stability of G[B,C],can be obtained if that of its subsetH[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>∈G[B,C],a<sub>ij</sub>=b<sub>ij</sub> or c<sub>ij</sub>}. （2）展开更多
Ⅰ. INTRODUCTION The stability of interval matrices has recently been studied and many results have been obtained. Consider n×n-dimensional real matrices P=(Pij) and Q=(qij), satisfying Pij≤qij and define N[P, Q...Ⅰ. INTRODUCTION The stability of interval matrices has recently been studied and many results have been obtained. Consider n×n-dimensional real matrices P=(Pij) and Q=(qij), satisfying Pij≤qij and define N[P, Q]={A=(aij)∈Rn×n|pij≤αij≤qij, i, j=1, 2…, n,}. The interval matrix N[P, Q] is said to be stable if A展开更多
This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞ norm of a transfer function to the Riccati matrixinequality and Hamilton matrix, sever...This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞ norm of a transfer function to the Riccati matrixinequality and Hamilton matrix, several test conditions with parameter perturbation bounds are obtained.展开更多
This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we obser...This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we observe that the conclusions of Perron-Frobenius theorem will hold if it holds for the starting matrix of this family. Based on our observations, we develop a simple numerical technique for approximating the Perron’s eigenpair of a given positive matrix. We apply the techniques introduced in the paper to approximate the Perron’s interval eigenvalue of a given positive interval matrix.展开更多
In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operatio...In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operation of sets (namely, Minkowski addition) in Boolean space B<sup>n</sup> are presented. Also, sums and multisums of various “classical figures” as: sphere, layer, interval etc. are considered. The obtained results make possible to describe multisums by such characteristics of summands as: the sphere radius, weight of layer, dimension of interval etc. using the methods presented in [2], as well as possible solutions of the equation X+Y=A, where , are considered. In spite of simplicity of the statement of the problem, complexity of its solutions is obvious at once, when the connection of solutions with constructions of equidistant codes or existence the Hadamard matrices is apparent. The present paper submits certain results (statements) which are to be the ground for next investigations dealing with Minkowski summation operations of sets in Boolean space.展开更多
文摘In this paper,the authors discuss the measure of interval matrices and its applications.The authors give a new method of the stability of interval matrices and get some sufficient and neessary conditions for it.These results are contained in work [4-9].
文摘Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.
文摘For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij</sub>},（1）B=(b<sub>ij</sub>)<sub>n×n</sub>=B<sup>T</sup>,C=(c<sub>ij</sub>)<sub>n×n</sub>=C<sup>T</sup>∈R<sup>n×n</sup>,Bialas has studied the necessary and sufficient condi-tion of asymptotic stabilty of G[B,C].According to refs[2-6],the following result,the asympotic stability of G[B,C],can be obtained if that of its subsetH[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>∈G[B,C],a<sub>ij</sub>=b<sub>ij</sub> or c<sub>ij</sub>}. （2）
文摘Ⅰ. INTRODUCTION The stability of interval matrices has recently been studied and many results have been obtained. Consider n×n-dimensional real matrices P=(Pij) and Q=(qij), satisfying Pij≤qij and define N[P, Q]={A=(aij)∈Rn×n|pij≤αij≤qij, i, j=1, 2…, n,}. The interval matrix N[P, Q] is said to be stable if A
文摘This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞ norm of a transfer function to the Riccati matrixinequality and Hamilton matrix, several test conditions with parameter perturbation bounds are obtained.
文摘This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we observe that the conclusions of Perron-Frobenius theorem will hold if it holds for the starting matrix of this family. Based on our observations, we develop a simple numerical technique for approximating the Perron’s eigenpair of a given positive matrix. We apply the techniques introduced in the paper to approximate the Perron’s interval eigenvalue of a given positive interval matrix.
文摘In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operation of sets (namely, Minkowski addition) in Boolean space B<sup>n</sup> are presented. Also, sums and multisums of various “classical figures” as: sphere, layer, interval etc. are considered. The obtained results make possible to describe multisums by such characteristics of summands as: the sphere radius, weight of layer, dimension of interval etc. using the methods presented in [2], as well as possible solutions of the equation X+Y=A, where , are considered. In spite of simplicity of the statement of the problem, complexity of its solutions is obvious at once, when the connection of solutions with constructions of equidistant codes or existence the Hadamard matrices is apparent. The present paper submits certain results (statements) which are to be the ground for next investigations dealing with Minkowski summation operations of sets in Boolean space.
