Related papers: Stability Theorems for Forbidden Configurations
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
Consider a matroid $M$ whose ground set is equipped with a labeling to an abelian group. A basis of $M$ is called $F$-avoiding if the sum of the labels of its elements is not in a forbidden label set $F$. H\"orsch, Imolay, Mizutani, Oki,…
The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generalization to this delay differential equation. The equation…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…
The space of stability conditions on a triangulated category is naturally partitioned into subsets $U(A)$ of stability conditions with a given heart $A$. If $A$ has finite length and $n$ simple objects then $U(A)$ has a simple geometry,…
We study an extremal projection principle for families of operators ordered by domination, induced by fixed bounded linear mappings acting on a source with an additive baseline. Stability is defined through domination of second--order…
Given a parameter dependent fixed point equation $x = F(x,u)$, we derive an abstract compactness principle for the fixed point map $u \mapsto x^*(u)$ under the assumptions that (i) the fixed point equation can be solved by the contraction…
Recent developments in data-driven control have revived interest in the behavioral approach to systems theory, where systems are defined as sets of trajectories rather than being described by a specific model or representation. However,…
Stability and stabilization analysis of fractional-order linear time-invariant (FO-LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single-order equivalent…
Inspired by the issue of stability of molecular structures, we investigate the strict minimality of point sets with respect to configurational energies featuring two- and three-body contributions. Our main focus is on characterizing those…
Federated learning is a distributed learning paradigm where multiple agents, each only with access to local data, jointly learn a global model. There has recently been an explosion of research aiming not only to improve the accuracy rates…
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices…
The stability number of a forbidden family measures how many different structures are needed to approximate all near-extremal constructions avoiding it. An infinite stability number means that no finite list of structures suffices. We…
The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…
In this paper, we consider the problem of computing the nearest stable matrix to an unstable one. We propose new algorithms to solve this problem based on a reformulation using linear dissipative Hamiltonian systems: we show that a matrix…