共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
In this article, based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain some new criteria ensuring mean square stability of trivial solution of a class of impulsive stochastic differential equations with delays. As an application, a class of stochastic impulsive neural network with delays has been discussed. One illustrative example has been provided to show the effectiveness of our results. 相似文献
3.
4.
Yuan-Chuan Li 《Linear algebra and its applications》2008,428(10):2319-2323
We study the joint spectral radius given by a finite set of compact operators on a Hilbert space. It is shown that the normed finiteness property holds in this case, that is, if all the compact operators are contractions and the joint spectral radius is equal to 1 then there exists a finite product that has a spectral radius equal to 1. We prove an additional statement in that the requirement that the joint spectral radius be equal to 1 can be relaxed to the asking that the maximum norm of finite products of a length norm is equal to 1. The length of this product is related to the dimension of the subspace on which the set of operators is norm preserving. 相似文献
5.
In this paper the problem of exponential stability of the zero state equilibrium of a discrete-time time-varying linear equation
described by a sequence of linear positive operators acting on an ordered finite dimensional Hilbert space is investigated.
The class of linear equations considered in this paper contains as particular cases linear equations described by Lyapunov
operators or symmetric Stein operators as well as nonsymmetric Stein operators. Such equations occur in connection with the
problem of mean square exponential stability for a class of difference stochastic equations affected by independent random
perturbations and Markovian jumping as well us in connection with some iterative procedures which allow us to compute global
solutions of discrete time generalized symmetric or nonsymmetric Riccati equations.
The exponential stability is characterized in terms of the existence of some globally defined and bounded solutions of some
suitable backward affine equations (inequalities) or forward affine equations (inequalities). 相似文献
6.
Yung-Yih Lur 《Linear algebra and its applications》2006,418(1):336-346
Let Ψ be a bounded set of n × n nonnegative matrices in max algebra. In this paper we propose the notions of the max algebra version of the generalized spectral radius μ(Ψ) of Ψ, and the max algebra version of the joint spectral radius η(Ψ) of Ψ. The max algebra version of the generalized spectral radius theorem μ(Ψ) = η(Ψ) is established. We propose the relationship between the generalized spectral radius ρ(Ψ) of Ψ (in the sense of Daubechies and Lagarias) and its max algebra version μ(Ψ). Moreover, a generalization of Elsner and van den Driessche’s lemma is presented as well. 相似文献
7.
This paper studies the solution of the spectral factorization problem for multivariable distributed parameter systems with an impulse response having an infinite number of delayed impulses. A coercivity criterion for the existence of an invertible spectral factor is given for the cases that the delays are a) arbitrary (not necessarily commensurate) and b) equally spaced (commensurate); for the latter case the criterion is applied to a system consisting of two parallel transmission lines without distortion. In all cases, it is essentially shown that, under the given criterion, the spectral density matrix has a spectral factor whenever this is true for its singular atomic part, i.e. its series of delayed impulses (with almost periodic symbol). Finally, a small-gain type sufficient condition is studied for the existence of spectral factors with arbitrary delays. The latter condition is meaningful from the system theoretic point of view, since it guarantees feedback stability robustness with respect to small delays in the feedback loop. Moreover its proof contains constructive elements. 相似文献
8.
This paper is devoted to discuss the exponential stability in mean square of neutral stochastic delayed systems (NSDDs) with switching and distributed-delay dependent impulses. By using multiple Lyapunov functions and average dwell time (ADT), we provide some sufficient conditions for the exponential stability in mean square for NSDDs with switching and distributed-delay dependent impulses. Compared with the existing related works, we consider not only the influences of switches and neutral type on the stability of NSDDs with switching and distributed-delay dependent impulses but also the influences of both the stable continuous dynamics case and the stable discrete dynamics case. Finally, we provide two examples to illustrate the effectiveness of the theory. 相似文献
9.
The notion of “strong stability” has been introduced in a recent paper [12]. This notion is relevant for state-space models described by physical variables and prohibits overshooting trajectories in the state-space transient response for arbitrary initial conditions. Thus, “strong stability” is a stronger notion compared to alternative definitions (e.g. stability in the sense of Lyapunov or asymptotic stability). This paper defines two distance measures to strong stability under absolute (additive) and relative (multiplicative) matrix perturbations, formulated in terms of the spectral and the Frobenius norm. Both symmetric and non-symmetric perturbations are considered. Closed-form or algorithmic solutions to these distance problems are derived and interesting connections are established with various areas in matrix theory, such as the field of values of a matrix, the cone of positive semi-definite matrices and the Lyapunov cone of Hurwitz matrices. The results of the paper are illustrated by numerous computational examples. 相似文献
10.
Victor Kozyakin 《Linear algebra and its applications》2010,433(1):12-4701
In 2002, Wirth has proved that the joint spectral radius of irreducible compact sets of matrices is locally Lipschitz continuous as a function of the matrix set. In the paper, an explicit formula for the related Lipschitz constant is obtained. 相似文献
11.
Lingsheng Shi 《Linear algebra and its applications》2007,422(1):58-66
The spectral radius of a (directed) graph is the largest eigenvalue of adjacency matrix of the (directed) graph. We give the relation on the characteristic polynomials of a directed graph and its line graph, and obtain sharp bounds on the spectral radius of directed graphs. We also give the relation on the spectral radii of a graph and its line graph. As a consequence, the spectral radius of a connected graph does not exceed that of its line graph except that the graph is a path. 相似文献
12.
13.
In this paper, we consider a class of neutral stochastic partial differential equations with delays and Poisson jumps. Sufficient conditions for the existence and exponential stability in mean square as well as almost surely exponential stability of mild solutions are derived by means of the Banach fixed point principle. An example is provided to illustrate the effectiveness of the proposed result. 相似文献
14.
In this paper, we first give some invariant subspace results for collectively compact sets of operators in connection with
the joint spectral radius of these sets. We then prove that any collectively compact set M in algΓ satisfies Berger-Wang formula, where Γ is a complete chain of subspaces of X.
相似文献
15.
In this paper, we consider the following problem: of all tricyclic graphs or trees of order n with k pendant vertices (n,k fixed), which achieves the maximal signless Laplacian spectral radius?We determine the graph with the largest signless Laplacian spectral radius among all tricyclic graphs with n vertices and k pendant vertices. Then we show that the maximal signless Laplacian spectral radius among all trees of order n with k pendant vertices is obtained uniquely at Tn,k, where Tn,k is a tree obtained from a star K1,k and k paths of almost equal lengths by joining each pendant vertex to one end-vertex of one path. We also discuss the signless Laplacian spectral radius of Tn,k and give some results. 相似文献
16.
Maozhong Fang 《Linear algebra and its applications》2007,425(1):7-15
We prove an upper bound for the spectral radius of the Hadamard product of nonnegative matrices and a lower bound for the minimum eigenvalue of the Fan product of M-matrices. These improve two existing results. 相似文献
17.
Yoav Sharon 《Journal of Differential Equations》2007,233(1):136-150
We consider an affine control system whose vector fields span a third-order nilpotent Lie algebra. We show that the reachable set at time T using measurable controls is equivalent to the reachable set at time T using piecewise-constant controls with no more than four switches. The bound on the number of switches is uniform over any final time T. As a corollary, we derive a new sufficient condition for stability of nonlinear switched systems under arbitrary switching. This provides a partial solution to an open problem posed in [D. Liberzon, Lie algebras and stability of switched nonlinear systems, in: V. Blondel, A. Megretski (Eds.), Unsolved Problems in Mathematical Systems and Control Theory, Princeton Univ. Press, 2004, pp. 203-207]. 相似文献
18.
Bao-Xuan Zhu 《Linear algebra and its applications》2010,433(5):928-261
In this paper, we show that among all the connected graphs with n vertices and k cut vertices, the maximal signless Laplacian spectral radius is attained uniquely at the graph Gn,k, where Gn,k is obtained from the complete graph Kn-k by attaching paths of almost equal lengths to all vertices of Kn-k. We also give a new proof of the analogous result for the spectral radius of the connected graphs with n vertices and k cut vertices (see [A. Berman, X.-D. Zhang, On the spectral radius of graphs with cut vertices, J. Combin. Theory Ser. B 83 (2001) 233-240]). Finally, we discuss the limit point of the maximal signless Laplacian spectral radius. 相似文献
19.
In this article, we present new bounds for the zeros of polynomials depending on some estimates for the spectral norms and the spectral radii of the square and the cube of the Frobenius companion matrix. 相似文献
20.
The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories. 相似文献