a necessary condition for feedback stabilization abstract we give a new necessary condition for the existence of a static or dynamic continuous asymptotically stabilizing feedback control for the system x dot f x u we apply our condition to give an example of a system in r 3 which is small time locally controllable satisfies brockett s second and third condition and cannot be locally asymptotically stabilized by employing a static or dynamic continuous feedback law

necessary conditions of asymptotic stability for unilateral dynamical systems in this paper we develop a mathematical tool that can be used to state necessary conditions of asymptotic stability of isolated stationary solutions of a class of unilateral dynamical systems more precisely nonlinear evolution variational inequalities are considered instability criteria are also given applications can be found in mechanics or electrical circuits

necessary conditions for stability and attractivity of continuous systems considered in this paper are control systems of the form f x u for such systems a number of related necessary conditions for various forms of stability and attractivity are presented the paper starts by showing that brockett s necessary condition for stabilizability via smooth feedback still persists if is continuous and the class of allowable u increased to include continuous feedbacks using similar ideas to those used to prove the continuous brockett result again only assuming continuity of f and u necessary conditions are then derived for global attractivity and for ultimate boundedness

determination of the algebraic relations among special γ values in positive characteristic we devise a new criterion for linear independence over function fields using this tool in the setting of dual t motives we find that all algebraic relations among special values of the geometric r function over f q t are explained by the standard functional equations

arithmetic of characteristic p special l values recently the second author has associated a finite fq t module h to the carlitz module over a finite extension of fq t this module is an analogue of the ideal class group of a number field in this paper we study the galois module structure of this module h for cyclotomic extensions of fq t we obtain function field analogues of some classical results on cyclotomic number fields such as the p adic class number formula and a theorem of mazur and wiles about the fitting ideal of ideal class groups we also relate the galois module h to anderson s module of circular units and give a negative answer to anderson s kummer vandiver type conjecture these results are based on a kind of equivariant class number formula which refines the second author s class number formula for the carlitz module

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

on brockett s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback the necessity of brockett s condition for stabilizability of nonlinear systems by smooth feedback is shown by an argument based on properties of a degree for set valued maps to persist when the class of controls is enlarged to include discontinuous feedback

a metropolis algorithm combined with hooke jeeves local search method applied to global optimization abstract a hybridization of a recently introduced metropolis algorithm named the particle collision algorithm pca and the hooke jeeves local search method is applied to a testbed of global optimization functions and to real world chemical equilibrium nonlinear systems the results obtained by this method called hjpca are compared against those achieved by two state of the art global optimization methods c grasp and global hjpca performs better than both algorithms thus demonstrating its potential for other applications

extinction criteria in stage structured population models with impulsive culling we propose stage structured population models for species whose adult members are subject to culling with a view to understanding the culling regimes that are likely to result in eradication of the species a purely time dependent model is proposed in which culling occurs at particular discrete times not necessarily equally spaced then a reaction diffusion model is proposed for a situation in which the adults can diffuse in this model the culling is continuous in time but occurs only at particular discrete points in space such a model might be appropriate for pheromone trapping of insects for both models conditions are obtained that are sufficient for species eradication

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

asymptotic periodicity of a food limited diffusive population model with time delay abstract in this paper a general reaction diffusion food limited population model with time delay is proposed accordingly the existence and uniqueness of the periodic solutions for the boundary value problem and the asymptotic periodicity of the initial boundary value problem are considered finally the effect of the time delay on the asymptotic behavior of the solutions is given

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

topological properties of asymptotically stable sets topological properties of the domain of attraction for dynamical systems are investigated the main purpose of this paper is to prove that a compact asymptotically stable attractor of a dynamical system defined on a locally compact metric space is a deformation retract of its domain of attraction in a weak sense that is made precise under additional local assumptions the attractor can be shown to be a retract a deformation retract or a strong deformation retract the well known result that the domain of attraction of an asymptotically stable equilibrium is contractible follows as a corollary

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

technical communique retraction obstruction to time varying stabilization this paper addresses the problem of the global stabilization on a total space of a fiber bundle with a compact base space we prove that under mild assumptions existence of a continuous section and forward unicity of solutions no equilibrium of a continuous system defined on such a state space can be globally asymptotically uniformly stabilized using continuous time varying feedback

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

linear independence of gamma values in positive characteristic we investigate the arithmetic nature of special values of thakur s func tion field gamma function at rational points our main result is that all linear dependence relations over the field of algebraic functions are consequences of the anderson deligne thakur bracket relations

asymptotically stabilizing feedback controls and the nonlinear regulator problem continuous asymptotically stabilizing feedback controls are constructed for two dimensional and certain three dimensional small time locally controllable affine systems the lie products which de

on diffusive population models with toxicants and time delays in this article we study the global stability in reaction diffusion models for single species population growth under environmental toxicants with or without time delays the existence and uniqueness of a positive steady state solution are established in those models it is shown that as long as the magnitude of the instantaneous self limitation and toxicant effects is larger than that of the time delay effects in the model with delays the solution of both reaction diffusion systems has the same asymptotic behavior extinction or converging to the positive steady state solution depending on the growth rate of the species numerical simulations for both cases with or without time delays are demonstrated for the purpose of comparison

transcendence and drinfeld modules it has been ten years since v g drinfeld introduced in 3 the concept of elliptic a module which we now call drinfeld a module these modules are analogues of elliptic curves for global function field k and we have witnessed a beautiful algebraic theory gradually taking shape in 13 we have asked a few natural t ranscendence questions conjectures concerning these modules having in mind the analogue of the classical work of siegel schneider about elliptic integrals and based on evidences provided by the old papers of carlitz and wade cf 1 11 here in this article we will prove those conjectures we will show that indeed there is an interesting transcendence theory for each algebraic curve over a finite field fol lowing drinfeld we let m be a lattice in i e a finitely generated discrete a module in k and form

connected simple systems and the conley index of isolated invariant sets the object of this paper is to present new and simplified proofs for most of the basic results in the index theory for flows simple explicit formulae are derived for the maps which play a central role in the theory the presentation is self contained

local asymptotic feedback stabilization to a submanifold topological conditions abstract we consider the problem of local asymptotic feedback stabilization of a control system x f x u defined in r n to a compact connected oriented embedded codimension one submanifold p of r n using a continuous feedback law this generalizes the problem of local asymptotic feedback stabilization to a point which has been previously considered in the control theory literature it is natural to expect the topology of p to play a role in deciding whether or not local asymptotic stabilization to p of the system x f x u is feasible via continuous feedback and our aim in this paper is precisely to outline necessary conditions on the topology of p for stabilization via continuous feedback to be achievable

asymptotic stabilization of two dimensional real analytic systems abstract we investigate the local asymptotic stabilizability of a real analytic control system around an equilibrium point and give necessary and sufficient conditions for local asymptotic stabilization using continuous feedback

zeta functions periodic trajectories and the conley index abstract we use the conley index to produce a simple sufficient condition stated in terms of the betti numbers of the cohomology conley index for the existence of periodic orbits for flows which admit a cross section

conley index condition for asymptotic stability in this paper we use conley index theory to develop necessary conditions for stability of equilibrium and periodic solutions of nonlinear continuous time systems the conley index is a topological generalization of the morse theory which has been developed to analyze dynamical systems using topological methods in particular the conley index of an invariant set with respect to a dynamical system is defined as the relative homology of an index pair for the invariant set the conley index can then be used to examine the structure of the system invariant set as well as the system dynamics within the invariant set including system stability properties efficient numerical algorithms using homology theory have been developed in the literature to compute the conley index and can be used to deduce the stability properties of nonlinear dynamical systems

direct and inverse analysis of diffusive logistic population evolution with time delay and impulsive culling via integral transforms and hybrid optimization abstract motivated by the fact that several species act as a vector in the spread of human or livestock diseases many works propose mathematical formulations for the modeling of these populations most of them considering fickian dispersion and logistic like growth rates for the best use of these models in a real application of optimal population control the model parameters should be identified as accurately as possible for a given species population in this work this parameter identification problem is formulated as an inverse problem which is tackled with a combination of the generalized integral transform technique gitt for the direct problem solution and a hybrid stochastic deterministic procedure for the minimization of the defined objective function in the inverse analysis employing the differential evolution and the levenberg marquardt methods the direct problem solution with gitt and the inverse analysis are critically investigated in order to improve the computational performance of the inverse problem solution a second order semi analytical integration and a solution refinement scheme are proposed

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

topological obstructions to submanifold stabilization we consider the problem of local asymptotic feedback stabilization via a continuously differentiable feedback law of a control system x f x u defined in euclidean space rn with f being continuously differentiable to a compact connected oriented m dimensional submanifold m of rn with codimension strictly larger than one we obtain necessary conditions on the topology of m for such a stabilizing feedback law to exist this extends the work done in where only the codimension one case was treated we also briefly discuss the case where the control is only assumed continuous