We consider a class of systems with a cyclic structure that arises, among other examples, in dynamic models for certain biochemical reactions. We first show that a criterion for local stability, derived earlier in the literature, is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices. We then revisit a recent generalization of this criterio...

Using an LMI (linear matrix inequality) optimization approach, a stability criterion is obtained for the local stability of the positive equilibrium of a Lotka–Volterra system with delays. © 2004 Elsevier Ltd. All rights reserved.

We study the evolution of a single crack in an elastic body and assume that the crack path is known in advance. The motion of the crack tip is modeled as a rate-independent process on the basis of Griffith’s local energy release rate criterion. According to this criterion, the system may stay in a local minimum before it performs a jump. The goal of this paper is to prove existence of such an e...

In this paper we derive a condition for robust local stability of multilayer recurrent neural networks with two hidden layers. The stability condition follows from linking theory about linearization, robustness analysis of linear systems under nonlinear perturbation and matrix inequalities. A characterization of the basin of attraction of the origin is given in terms of the level set of a quadr...

The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implic...

This paper considers the problem of global asymptotic stability of a class of two-dimensional (2-D ) uncertain discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model under the influence of various combinations of quantization/overflow nonlinearities and interval-like time-varying delay in the state. The systems under consideration involve parameter uncert...

A Popov criterion is derived for systems with slowly timevarying parameters. The parameters and their time derivatives are assumed to take values in convex polytopes.

This paper reviews the problem of a thin rigid rod sliding on a horizontal surface in the plane, which is commonly cited as an example of the inconsistency of planar rigid-body Newtonian mechanics. We demonstrate the existence of a consistent solution, using Routh's analysis of rigid-body impact. Copyright © 1987 Carnegie-Mel lon University This work was supported under grants from the System D...

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