This paper offers necessary and sufficient condition for delay-dependent asymptotic stability of linear discrete systems with multiple time delay. The criterion is derived by Lyapunov’s direct method and two matrix equations have been obtained: discrete Lyapunov matrix equation for nondelay systems and polynomial matrix equation. Obtained stability condition does not possess conservatism but re...

Several notions of exponential stability of linear time-invariant systems on arbitrary time scales are discussed. We establish a necessary and sufficient condition for the existence of uniform exponential stability. Moreover, we characterize the uniform exponential stability of a system by the spectrum of its matrix. In general, exponential stability of a system can not be characterized by the ...

The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have me...

The necessary and sufficient condition for stability of K-symmetrizable interval matrix is given. An algorithm for checking stability of K-symmetrizable interval matrix is proposed.

We prove tight bounds for the ∞-norm of the inverse of symmetric diagonally dominant positive matrices. Applications include numerical stability for linear systems, bounds on inverses of differentiable functions, and the consistency of maximum entropy graph distributions from single samples.

When considering a social media corpus, we often have access to structural information about how messages are flowing between people or organizations. This information is particularly useful when the linguistic evidence is sparse, incomplete, or of dubious quality. In this paper we construct a simple model to leverage the structure of Twitter data to help determine the set of languages each use...

In the design of decentralized networked systems, it is useful to know whether a given network topology can sustain stable dynamics. We consider a basic version of this problem here: given a vector space of sparse real matrices, does it contain a stable (Hurwitz) matrix? Said differently, is a feedback channel (corresponding to a non-zero entry) necessary for stabilization or can it be done wit...

In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to...

Sum frequency generation and IR absorption spectra of CO adsorbed on Pd(111) are reported. Adsorption of CO in the surface temperature range 150–230 K results in the appearance of extra peaks in the spectral range of the CO stretching vibration. The conditions of appearance of these peaks, and their stability, are investigated. The extra peaks are assigned to sites at antiphase domain boundarie...

This paper develops a robust method to enumerate the incident signals impinging on a uniform but variable size linear array independant of their extent of correlation in a Rayleigh flat fading channel environment. The method also optimizes by minimizing the number of antennas to the number of signals and adapts continously to maintain optimum performance in a mobile environment where users (sig...