d stability and delay independent stability of homogeneous cooperative systems we introduce a nonlinear definition of d stability extending the usual concept for positive linear time invariant systems we show that globally asymptotically stable cooperative systems homogeneous of any order with respect to arbitrary dilation maps are d stable we also prove a strong stability result for delayed cooperative homogeneous systems finally we show that both of these results also hold for planar cooperative systems without the restriction of homogeneity

on the stability of the parallel sum of maximal monotone operators identifying operators with their graphs we study the continuity of the parallel sum of two monotone operators with respect to set convergence and we examine its stability from a quantitative point of view

power control in wireless networks stability and delay independence for a general class of distributed algorithms we show that for a general class of distributed power control algorithms in wireless networks if a feasible steady state power allocation exists this is asymptotically stable for arbitrary gains and time varying heterogeneous delays the analysis exploits certain contraction properties of the interference in such algorithms and makes use of lyapunov razumikhin functions to address the infinite dimensional character of the problem

perturbation of nonlinear operators and their parallel sum on donne une version de la formule de kubo a b s lime 0 a ei b ei pour a et b des operateurs non lineaires

convergent systems vs incremental stability two similar stability notions are considered one is the long established notion of convergent systems the other is the younger notion of incremental stability both notions require that any two solutions of a system converge to each other yet these stability concepts are different in the sense that none implies the other as is shown in this paper using two examples it is shown under what additional assumptions one property indeed implies the other furthermore this paper contains necessary and sufficient characterizations of both properties in terms of lyapunov functions

neat idempotents and tiled orders having large global dimension abstract we study neat primitive idempotents in a semiperfect noetherian ring and as an application we improve an example of a tiled order having large global dimension given by jansen and odenthal moreover another two tiled orders having large global dimension are added and two questions on tiled orders of finite global dimension are posed

delay independent incremental stability in time varying monotone systems satisfying a generalized condition of two sided scalability monotone systems generated by delay differential equations with explicit time variation are of importance in the modeling of a number of significant practical problems including the analysis of communications systems population dynamics and consensus protocols in such problems it is often of importance to be able to guarantee delay independent incremental asymptotic stability whereby all solutions converge toward each other asymptotically thus allowing the asymptotic properties of all trajectories of the system to be determined by simply studying those of some particular convenient solution it is known that the classical notion of quasimonotonicity renders time delayed systems monotone however this is not sufficient alone to obtain such guarantees in this work we show that by combining quasimonotonicity with a condition of scalability motivated by wireless networks it is possible to guarantee incremental asymptotic stability for a general class of systems that includes a variety of interesting examples furthermore we obtain as a corollary a result of guaranteed convergence of all solutions to a quantifiable invariant set enabling time invariant asymptotic bounds to be obtained for the trajectories even if the precise values of time varying parameters are unknown

enlargements and sums of monotone operators in this paper we study two important notions related to monotone operators one is the concept of enlargement of a given monotone operator which has turned out to be a useful tool in the analysis of approximate solutions to problems involving monotone operators the second one is the notion of sum of monotone operators for the latter we introduce and study a kind of extended sum of two monotone operators which in several important cases turns out to be a maximal monotone operator

direct and inverse addition in convex analysis and applications abstract inspired simultaneously from the theory of network synthesis and from the theory of means for positive operators we introduce the notions of direct and inverse addition of order p for pairs of convex sets in a locally convex topological linear space in this way a general formalism is introduced which allows us on the one hand to recover the operations of series and parallel addition derived from network connections as well as the notions of arithmetic and harmonic means for positive operators and on the other hand to recover the main binary operations on convex sets appearing in convex analysis

convergent dynamics a tribute to boris pavlovich demidovich we review and pay tribute to a result on convergent systems by the russian mathematician boris pavlovich demidovich in a sense demidovich s approach forms a prelude to a field which is now called incremental stability of dynamical systems developments on incremental stability are reviewed from a historical perspective

a tiled order having large global dimension abstract the finite global dimension of a tiled order over a discrete valuation ring is bounded by a function of the uniform dimension of the order but the exact form of the function is unknown let n be the uniform dimension a conjecture t1 that the bound is n 1 was disproved f2 by producing an example of global dimension n we construct for any even n 8 a tiled order of uniform dimension n having global dimension 2 n 8

the max plus algebra of exponent matrices of tiled orders abstract an exponent matrix is an n n matrix a a i j over n 0 satisfying 1 a i i 0 for all i 1 n and 2 a i j a j k a i k for all pairwise distinct i j k 1 n in the present paper we study the set e n of all non negative n n exponent matrices as an algebra with the operations of component wise maximum and of component wise addition we provide a basis of the algebra e n 0 and give a row and a column decompositions of a matrix a e n with respect to this basis this structure result determines all n n tiled orders over a fixed discrete valuation domain we also study automorphisms of e n with respect to each of the operations and and prove that aut e n 0 aut e n aut e n s n c 2 n 2

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

attractors in strongly monotone flows where f is a c vector field in r and all the off diagonal terms of its jacobian matrix are nonnegative the well known kamke theorem implies that the flow 4 i ir0 generated by 1 has the property it preserves the partial ordering 0 another system which has this property is the semilinear parabolic equation on a compact n dimensional submanifold solutions of its dirichlet or neumann problem determine a monotone flow in appropriate function space see 11 or 51 in general a flow which preserves a partial ordering on the state space is called monotone m w hirsch has studied this flow in a series of papers 14 io he 2 31 has studied the limiting behavior and convergence of solutions of system 1 he 1 4 lo has investigated this flow in the considerably abstract state space in chapter iii of cl he has used two sections to discuss the properties of attractors for monotone flows and obtained some very important results he has shown that a monotone flow cannot have an attracting cycle see l corollary 2 41 and that every attractor must contain an equilibrium see cl theorem 3 11 in particular if the flow is strongly monotone he has shown that every attractor k contains an order stable equilibrium see 1 theorem 4 11 meanwhile if we suppose z is attracted to k but is not quasiconvergent then k contains two order stable equilibria p q such that p o z 4 q see cl theorem 4 31 the purpose of this paper is further to discuss the properties of attractors for strongly monotone flows we shall study when an o limit set can be an 210 0022 247x 91 3 00

continuous control lyapunov functions for asymptotically controllable time varying systems this paper shows that for time varying systems global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control lyapunov function with respect to the set

a differential lyapunov framework for contraction analysis lyapunov s second theorem is an essential tool for stability analysis of differential equations the paper provides an analog theorem for incremental stability analysis by lifting the lyapunov function to the tangent bundle the lyapunov function endows the state space with a finsler structure incremental stability is inferred from infinitesimal contraction of the finsler metrics through integration along solutions curves

what shape is your conjugate a survey of computational convex analysis and its applications computational convex analysis algorithms have been rediscovered several times in the past by researchers from different fields to further communications between practitioners we review the field of computational convex analysis which focuses on the numerical computation of fundamental transforms arising from convex analysis current models use symbolic numeric and hybrid symbolic numeric algorithms our objective is to disseminate widely the most efficient numerical algorithms useful for applications in image processing computing the distance transform the generalized distance transform and mathematical morphology operators partial differential equations solving hamilton jacobi equations and using differential equations numerical schemes to compute the convex envelope max plus algebra computing the equivalent of the fast fourier transform multifractal analysis etc the fields of applications include among others computer vision robot navigation thermodynamics electrical networks medical imaging and network communication

asymptotic properties of incrementally stable systems it is shown that incremental stability of an input output operator ensures asymptotic stability of any equilibrium pair x sub e u sub e of its state representation if suitable minimality assumptions hold

the parallel sum of nonlinear monotone operators on definit la somme parallele d operateurs non lineaires dans un espace de hilbert a l aide de leurs graphes

the behavior of incrementally stable discrete time systems abstract this paper focus on the behavior analysis of incrementally bounded lipschitz continuous systems on l p with p 1 we first establish the properties of the motions which are associated with all inputs inside l p e with respect to a modification of the initial condition as a matter of fact under some minimality properties of the state space realization of the system we prove the lyapunov stability of all unperturbed motions as a second point we investigate the properties of the motions obtained when the input is perturbed either by perturbations which go to zero at the infinity or by perturbations with a bounded magnitude all these results are obtained through the reformulation of the incremental boundedness of a system in terms of the dissipativity of an associated fictitious system

consensus problems on networks with antagonistic interactions in a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents expresses by a communication graph with nonnegative weights the question we ask in this paper is the following is it possible to achieve a form of agreement also in presence of antagonistic interactions modeled as negative weights on the communication graph the answer to this question is affirmative on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign necessary and sufficient conditions are obtained to describe cases in which this is possible these conditions have strong analogies with the theory of monotone systems linear and nonlinear laplacian feedback designs are proposed