point island dynamics under fixed rate deposition abstract we consider the dynamics of point islands during submonolayer deposition in which the fragmentation of subcritical size islands is allowed to understand asymptotics of solutions we use methods of centre manifold theory and for globalisation we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems we also compare our results with those obtained by making the quasi steady state assumption

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

on the decay rate of discrete time linear delay systems with cone invariance this technical note is concerned with the decay rate constrained stability analysis for linear delay systems that possess cone invariant property in order to capture the decay rate of such systems we introduce a nondecreasing positive function whose reciprocal represents the decay rate under mild assumptions on the growth rate of this function an explicit condition is given to ensure that a cone preserving linear system with unbounded time varying delays is asymptotically stable with a given decay rate as typical cases necessary and sufficient conditions are given to characterize the decay rate when the delay is restricted by a linear sublinear or logarithmic growth rate finally some numerical examples are given to illustrate the effectiveness of the theoretical results

large assemblies of stochastic oscillators this paper studies the occurrence of stochastic synchronization and phase locking in large assemblies of coupled stochastic oscillators which are modelled as phaseangle stochastic processes attention will be restricted to the case of discrete phaseangle spaces these are technically much simpler than processes over continuous phase spaces and yet show an interesting range of properties stochastic synchronization occurs if the oscillator assembly obeys a large deviation principle and if the deterministic limit dynamics possesses a stable periodic orbit all relevant concepts are reviewed in section section 1 2 and the appendix in section 4 general necessary and sufficient conditions for stochastic synchronization are obtained weak and robust types of synchronization are distinguished a describing function method is formulated which is very convenient for checking the general conditions in concrete examples separate treatments of feedback gain feedback type i e positive or negative and feedback sources lead to investigations of how the occurrence of stochastic synchronization depends on any one of those feedback aspects in a sequence of gradually more realistic models section 3 4b 5a the general results are applied to assemblies of stochastic fireflies the first of these models section 3 is mathematically instructive in that it provides a good example of how the liapunov function character of large deviation rate functions can be exploited to study global properties of the corresponding deterministic limit ode the analysis of firefly assemblies culminates in a proof of stochastic firefly synchronization this result is the precise stochastic analogue of the well known proof of deterministic firefly synchronization given by mirollo strogatz 1990 in section 5 the general results of section 4 are applied to neuronal assemblies particular attention is paid to the dependence of neuronal synchronization on the feedback type that is excitatory or inhibitory signalling we find it natural and instructive to distinguish between external and internal variants of inhibition the latter in particular in the form of graded refractoriness of neurons is shown to be crucial for stochastic synchronization within one neural assembly whereas the former is instrumental for phase locking between distinct assemblies these findings are summarized and sharpened in a number of concrete predictions for real biological networks of neurons except for some topical aspects of large deviation theory reviewed in the appendix the mathematics employed in this paper are straightforward

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

composite systems with uncertain couplings of fixed structure scaled riccati equations and the problem of quadratic stability we consider large scale systems consisting of a finite number of separate uncertain subsystems which interact via uncertain couplings of arbitrarily prescribed structure the couplings are viewed as structured perturbations of the block diagonal system representing the collection of the separate nominal subsystems the nominal system we define spectral value sets and stability radii for these time invariant structured perturbations and derive formulas for their computation scaled riccati equations are introduced to obtain explicit formulas for the stability radii with respect to time varying and possibly nonlinear perturbations of the given structure from these we derive necessary and sufficient conditions under which the stability radii with respect to time invariant and time varying perturbations are equal these results are obtained by constructing joint quadratic liapunov functions of optimal robustness with their help we prove necessary and sufficient conditions for quadratic stability and sufficient conditions for the validity of a generalized aizerman conjecture

on the minus partial order in control systems abstract in this paper the minus matrix partial order is considered to introduce the concept of minus partial ordered control systems the transmission of the reachability property under this binary relation is investigated furthermore the analysis of compartmental systems leads us to consider block triangular matrices hence the existence and computation of partially ordered matrices having a similar block structure are studied these results are applied to compartmental systems to get via feedback related systems with the same block structure and ordered under the minus partial order

realization of continuous time positive linear systems positive linear systems are used in biomathematics economics and other research areas for discrete time positive linear systems part of the realization problem has been solved in this paper the solution of the corresponding problem for continuous time positive linear systems will be presented which can be deduced from that of the discrete time case by a transformation sufficient and necessary conditions for the existence of a positive realization are presented to solve the problem of minimality the solution of the factorization of positive matrices is needed

necessary and sufficient conditions for stabilizability of positive lti systems this paper obtains necessary and sufficient conditions for the stabilization of positive lti systems using a vertex algorithmic approach the results of this paper also encompass positive direct output feedback control the topic of the sequential separation principle and a particularly efficient algorithm for a class of positive systems

technical communique adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental models are widespread in engineering systems and life sciences and play a key role in the understanding of these systems in this paper we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental dynamical systems the proposed framework is lyapunov based and guarantees partial asymptotic set point regulation that is asymptotic set point regulation with respect to part of the closed loop system states associated with the plant in addition the adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space

brief paper on linear co positive lyapunov functions for sets of linear positive systems in this paper we derive necessary and sufficient conditions for the existence of a common linear co positive lyapunov function for a finite set of linear positive systems both the state dependent and arbitrary switching cases are considered our results reveal an interesting characterisation of linear stability for the arbitrary switching case namely the existence of such a linear lyapunov function can be related to the requirement that a number of extreme systems are metzler and hurwitz stable examples are given to illustrate the implications of our results

on the dynamics of a class of multi group models for vector borne diseases abstract the resurgence of vector borne diseases is an increasing public health concern and there is a need for a better understanding of their dynamics for a number of diseases e g dengue and chikungunya this resurgence occurs mostly in urban environments which are naturally very heterogeneous particularly due to population circulation in this scenario there is an increasing interest in both multi patch and multi group models for such diseases in this work we study the dynamics of a vector borne disease within a class of multi group models that extends the classical bailey dietz model this class includes many of the proposed models in the literature and it can accommodate various functional forms of the infection force for such models the vector host host vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases under the assumption that the contact network is strongly connected we can define the basic reproductive number r 0 and show that this system has only two equilibria the so called disease free equilibrium dfe and a unique interior equilibrium usually termed the endemic equilibrium ee that exists if and only if r 0 1 we also show that if r 0 1 then the dfe equilibrium is globally asymptotically stable while when r 0 1 we have that the ee is globally asymptotically stable

localization and periodicity in unstable homotopy theory in this paper we develop a hierarchy of natural localizations of spaces called the vn periodizations for n 0 which may be used to expose and study periodic phenomena in unstable homotopy theory these vn periodizations act less radically than the corresponding homological localizations 2 and respect fibrations to a very considerable extent a major part of this paper is devoted to developing the general theory of periodizations of spaces thereby providing a foundation for the study of the vn periodization and many others some of this general theory has been developed independently by dror farjoun 13 14 and we refer the reader to his work for an alternative approach with other interesting general results during the past decade remarkable progress was made by ravenel hopkins devinatz and smith 12 16 17 33 toward a global understanding of stable periodic phenomena and we hope that the present paper will help to prepare the way for a similar understanding of unstable periodic phenomena an excellent exposition of localization and periodicity in stable homotopy theory is now available in ravenel s book 35 major features of stable homotopy are understood chromatically as manifestations of more basic periodic phenomena these phenomena belong to a hierarchy starting with those detected rationally followed by those detected in classical k theory and in the successive morava k theories most fundamentally each finite cw spectrum has an intrinsic periodicity given by a vn self map which becomes a selfequivalence after suitable localization for simplicity we describe our results in the pointed homotopy category hoo of connected cw complexes for spaces w y e hoo we call y w periodic or w local when the pointed mapping space map w y is contractible or equivalently when xt w y for t 0 as shown more generally in 3 corollary 7 2 10 or 13 there is a natural initial example x pwx of a map from x to a w periodic space pwx in hoo and we call this the w periodization or w localization of x our notation is derived from the classical example where w sn l and pwx is the n th postnikov section

on the youla kucera parametrization for nonlinear systems abstract we consider the problem of stabilizing a nonlinear plant through the use of a possibly unstable pre compensator and a stable feedback compensator and parameterizing a class of such stabilizers in terms of a bibo stable map q in the linear case by means of superposition the pre and feedback compensator can be combined in such a way that the bibo map q occurs in just one feedback loop within the controller feeding back output residuals prediction errors to the control inputs the main contribution of this paper is to develop a nonlinear generalization of this property building on earlier work in forming the youla kucera parametrization for nonlinear systems we show the equivalence of the class of all bounded input stabilizing nonlinear pre and feedback compensators to a class of possibly unstable feedback controllers in which a map q s is present in only the one feedback loop we then show that necessary and sufficient condition to achieve stability of the system is that q s be bibo stable one advantage of the new formulation is that differential boundedness assumptions do not involve the parametrization q s in any way just as the linear versions of our results have applications in the areas of optimal control and adaptive control of linear systems it is conjectured that the present results will underlie more general results for adaptive control and nonlinear systems

mu stability of nonlinear positive systems with unbounded time varying delays the stability of the zero solution plays an important role in the investigation of positive systems in this brief we discuss the mu stability of positive nonlinear systems with unbounded time varying delays the system is modeled by the continuous time ordinary differential equation under some assumptions on the nonlinear functions such as homogeneous cooperative and nondecreasing we propose a novel transform by which the nonlinear system reduces to a new system thus we analyze its dynamics which can simplify the nonlinear homogenous functions with respect to the arbitrary dilation map to those with respect to the standard dilation map we finally get some new criteria for the global mu stability taking the degree into consideration a numerical example is given to demonstrate the validity of obtained results

neural network adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous in this paper we develop a full state feedback neural adaptive control framework for adaptive set point regulation of nonlinear uncertain nonnegative and compartmental systems the proposed framework is lyapunov based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains in addition the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions

global analysis of a schistosomiasis infection model with biological control in this paper the global stability of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mammalian host and a competitor snail species is studied by constructing lyapunov functions and using properties of k monotone systems we derive the basic reproduction number r 0 for the deterministic model and establish that the global dynamics are completely determined by the values of r 0 we show that the disease can be eradicated when r 0 1 in the case where r 0 1 we prove the existence uniqueness and global asymptotic stability of an endemic steady state this mathematical analysis of the model gives insight about the epidemiological consequences of the introduction of a competitor resistant snail species

asymptotic behavior of solutions of nonautonomous neutral dynamical systems abstract this paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator of great importance for their applications to the study of the long term behavior of the trajectories of problems described by this kind of equations such us compartmental systems and neural networks among many others precisely more general admissible initial conditions are included in the study to show that the solutions are asymptotically of the same type as the coefficients of the neutral and non neutral part

homotopical localizations of spaces for a map f of spaces dror farjoun and the author have constructed an f localization functor where a space y is called f local when map f y is an equivalence this very general construction gives all known idempotent homotopy functors of spaces the main theorem of this paper shows that f localization functors always preserve fiber sequences of connected h spaces up to small error terms for instance the localization with respect to the n th morava k theory preserves such fiber sequences up to error terms with at most three nontrivial homotopy groups this implies for example that a k 1 homology equivalence of h spaces must induce an isomorphism of v 1 periodic homotopy groups results are also obtained on the a nullification or a periodization functors which are just the f localization functors for the maps f from spaces a to points two spaces are said to have the same nullity when they give the same nullification functors and it is shown that arbitrary sets of nullity classes have both least upper bounds and greatest lower bounds the a nullifications of nilpotent postnikov spaces are completely determined

spectral conditions for stability and stabilization of positive equilibria for a class of nonlinear cooperative systems nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication biological economical and neural network applications for this class of positive systems we provide conditions that guarantee existence uniqueness and stability of strictly positive equilibria these conditions can be formulated directly in terms of the spectral radius of the jacobian of the system if control inputs are available then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant

nonlinear unity feedback systems and q parametrization this paper concerns nonlinear systems defines a new concept of stability and extends to unity feedback systems the technique of q parametrization introduced by zames and developed by desoer chen and gustafson we specify 1 a global parametrization of all controllers that s stabilize a given s stable plant 2 a parametrization of a class of controllers that stabilize an unstable plant 3 necessary and sufficient conditions for a nonlinear controller to simultaneously stabilize two nonlinear plants

on the telescopic homotopy theory of spaces in telescopic homotopy theory a space or spectrum x is approximated by a tower of localizations lnx n 0 taking account of vn periodic homotopy groups for progressively higher n for each n 1 we construct a telescopic kuhn functor n carrying a space to a spectrum with the same vn periodic homotopy groups and we construct a new functor n left adjoint to n using these functors we show that the nth stable monocular homotopy category comprising the nth fibers of stable telescopic towers embeds as a retract of the nth unstable monocular homotopy category in two ways one giving infinite loop spaces and the other giving infinite ln suspension spaces we deduce that ravenel s stable telescope conjectures are equivalent to unstable telescope conjectures in particular we show that the failure of ravenel s nth stable telescope conjecture implies the existence of highly connected infinite loop spaces with trivial johnson wilson e n homology but nontrivial vn periodic homotopy groups showing a fundamental difference between the unstable chromatic and telescopic theories as a stable chromatic application we show that each spectrum is k n equivalent to a suspension spectrum as an unstable chromatic application we determine the e n localizations and k n localizations of infinite loop spaces in terms of e n localizations of spectra under suitable conditions we also determine the e n localizations and k n localizations of arbitrary postnikov h spaces

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

output to state stability and detectability of nonlinear systems the notion of input to state stability iss has proved to be useful in nonlinear systems analysis this paper discusses a dual notion output to state stability oss a characterization is provided in terms of a dissipation inequality involving storage lyapunov functions combining iss and oss there results the notion of input output to state stability ioss which is also studied and related to the notion of detectability the existence of observers and output injection

a state space approach to parameterization of stabilizing controllers for nonlinear systems a state space approach to the youla parameterization of stabilizing controllers for linear and nonlinear systems is suggested the stabilizing controllers or a class of stabilizing controllers for nonlinear systems are characterized as fractional transformations of stable parameters the main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems the parameterized output feedback controllers have separation structures this machinery allows the parameterization of stabilizing controllers to be conducted directly in state space without using coprime factorization

asymptotic stability and decay rates of homogeneous positive systems with bounded and unbounded delays there are several results on the stability of nonlinear positive systems in the presence of time delays however most of them assume that the delays are constant this paper considers time varying possibly unbounded delays and establishes asymptotic stability and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case specifically we present a necessary and sufficient condition for delay independent stability of continuous time positive systems whose vector fields are cooperative and homogeneous we show that global asymptotic stability of such systems is independent of the magnitude and variation of the time delays for various classes of time delays we are able to derive explicit expressions that quantify the decay rates of positive systems we also provide the corresponding counterparts for discrete time positive systems whose vector fields are nondecreasing and homogeneous

stability and stabilizability of continuous time linear compartmental switched systems in this paper we introduce continuous time linear compartmental switched systems and investigate their stability and stabilizability properties by their nature these systems are always stable necessary and sufficient conditions for asymptotic stability for arbitrary switching functions and sufficient conditions for asymptotic stability under certain dwell time conditions on the switching functions are proposed finally stabilizability is thoroughly investigated and proved to be equivalent to the existence of a hurwitz convex combination of the subsystem matrices a condition that for positive switched systems is only sufficient for stabilizability

on the reachable set for third order linear discrete time systems with positive control the case of complex eigenvalues abstract in this paper we study the geometrical properties of the set of reachable states of a single input third order discrete time linear system with positive controls this set is a cone and we give a complete geometrical characterization of this set when the system has a complex conjugate pair of eigenvalues more in detail we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations

dynamically consistent nonstandard finite difference schemes for epidemiological models this work is the numerical analysis and computational companion of the paper by kamgang and sallet j c kamgang g sallet computation of threshold conditions for epidemiological models and global stability of the disease free equilibrium dfe mathematical biosciences 213 2008 1 12 where threshold conditions for epidemiological models and the global stability of the disease free equilibrium dfe are studied we establish a discrete counterpart of the main continuous result that guarantees the global asymptotic stability gas of the dfe for general epidemiological models then we design nonstandard finite difference nsfd schemes in which the metzler matrix structure of the continuous model is carefully incorporated and both mickens rules world scientific singapore 1994 on the denominator of the discrete derivative and the nonlocal approximation of nonlinear terms are used in an innovative way as a result of these strategies our nsfd schemes are proved to be dynamically consistent with the continuous model i e they replicate their basic features including the gas of the dfe the linear stability of the endemic equilibrium ee the positivity of the solutions the dissipativity of the system and its inherent conservation law the general analysis is made detailed for the mseir model for which the nsfd theta method is implemented with emphasis on the computational aspects such as its convergence or local truncation error numerical simulations that illustrate the theory are provided

transit time and age distributions for nonlinear time dependent compartmental systems many processes in nature are modeled using compartmental systems reservoir pool box systems usually they are expressed as a set of first order differential equations describing the transfer of matter across a network of compartments the concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions until now explicit formulas for transit time and age distributions of nonlinear time dependent compartmental systems were not available we compute densities for these types of systems under the assumption of well mixed compartments assuming that a solution of the nonlinear system is available at least numerically we show how to construct a linear time dependent system with the same solution trajectory we demonstrate how to exploit this solution to compute transit time and age distributions in dependence on given start values and initial age distributions furthermore we derive equations for the time evolution of quantiles and moments of the age distributions our results generalize available density formulas for the linear time independent case and mean age formulas for the linear time dependent case as an example we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time dependent input signal which represents fossil fuel additions we derive time dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business as usual scenario

stabilization of positive linear systems we consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant the existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane this allows to transform the problem to the stabilization problem of compartmental systems which is known and for which a solution has been proposed already we provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback a class of stabilizing feedbacks is given explicitly

stability of traffic flow networks with a polytree topology we consider global stability of a flow network model for vehicular traffic standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions in this paper we show that the network model nonetheless exhibits a mixed monotonicity property mixed monotonicity allows us to prove global asymptotic stability by embedding the system in a larger system that is monotone

stability and dissipativity theory for discrete time non negative and compartmental dynamical systems non negative and compartmental dynamical systems are derived from mass and energy balance considerations that involve dynamic states whose values are non negative these models are widespread in engineering biomedicine and ecology in this paper we develop several results on stability dissipativity and stability of feedback interconnections of discrete time linear and non linear non negative dynamical systems specifically using linear lyapunov functions we first develop necessary and sufficient conditions for lyapunov stability and asymptotic stability for non negative systems in addition using linear and non linear storage functions with linear supply rates we develop new notions of dissipativity theory for non negative dynamical systems finally these results are used to develop general stability criteria for feedback interconnections of non negative dynamical systems

a class of globally stabilizing controllers for nonlinear systems abstract a class of globally stabilizing controllers for nonlinear systems are parametrized as fractional transformations on some input to state stable parameters

nontangency based lyapunov tests for convergence and stability in systems having a continuum of equilibria this paper focuses on the stability analysis of systems having a continuum of equilibria two notions that are of particular relevance to such systems are convergence and semistability convergence is the property whereby every solution converges to a limit point that may depend on the initial condition semistability is the additional requirement that all solutions converge to limit points that are lyapunov stable we give new lyapunov function based results for convergence and semistability of nonlinear systems these results do not make assumptions of sign definiteness on the lyapunov function instead our results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite lyapunov functions to illustrate our results we deduce convergence and semistability of the kinetics of the michaelis menten chemical reaction and the closed loop dynamics of a scalar system under a universal adaptive stabilizing feedback controller

a convex characterization of robust stability for positive and positively dominated linear systems we provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems in particular we show that the structured singular value is always equal to its convex upper bound for nonnegative matrices and we use this result to derive necessary and sufficient linear matrix inequality lmi conditions for robust stability that involve only the system s static gain we show how this approach can be applied to test the robust stability of the foschini miljanic algorithm for power control in wireless networks in presence of uncertain interference

correction to structure and stability of certain chemical networks and applications to the kinetic proofreading model of t cell receptor signal transduction deals with the theory of structure stability robustness and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks the results given here extend but are also heavily based upon certain previous work by feinberg 1977 1979 1987 1995 and horn and jackson 1972 of which a self contained and streamlined exposition is included the theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by mckeithan 1995 for t cell receptor signal transduction

moving horizon estimation for large scale interconnected systems we present computationally efficient centralized and distributed moving horizon estimation mhe methods for large scale interconnected systems that are described by sparse banded or sparse multibanded system matrices both of these mhe methods are developed by approximating a solution of the mhe problem using the chebyshev approximation method by exploiting the sparsity of this approximate solution we derive a centralized mhe method which computational complexity and storage requirements scale linearly with the number of local subsystems of an interconnected system furthermore on the basis of the approximate solution of the mhe problem we develop a novel distributed mhe method this distributed mhe method estimates the state of a local subsystem using only local input output data in contrast to the existing distributed algorithms for the state estimation of large scale systems the proposed distributed mhe method is not relying on the consensus algorithms and has a simple analytic form we have studied the stability of the proposed mhe methods and we have performed numerical simulations that confirm our theoretical results

the dynamical systems approach to differential equations bulletin new series of the american mathematical society volume 11 number 1 july 1984 the dynamical systems approach to differential equations by morris w hirsch 1 this harmony that human intelligence believes it discovers in nature does it exist apart from that intelligence no without doubt a reality completely independent of the spirit which conceives it sees it or feels it is an impossibility a world so exterior as that even if it existed would be forever inaccessible to us but what we call objective reality is in the last analysis that which is common to several thinking beings and could be common to all this common part we will see can be nothing but the harmony expressed by mathematical laws h poincare la valeur de la science p 9 ignorance of the roots of the subject has its price no one denies that modern formulations are clear elegant and precise it s just that it s impossible to comprehend how any one ever thought of them m spivak a comprehensive introduction to differential geometry introduction the mathematical subject we call dynamical systems was fathered by poin care developed sturdily under birkhoff and has enjoyed a vigorous new growth for the last twenty years as i try to show in chapter i it is interesting to look at this mathematical development as the natural outcome of a much broader theme which is as old as science itself the universe is a sytem which changes in time every mathematician has a particular way of thinking about mathematics but rarely makes it explicit yet such perspectives in any particular field can be of great value to nonexperts who must apply the results of the field or who want to learn them in some fields the points of view of its practitioners cluster around several comparatively clearly defined concepts and insights dynamical systems theory is one of them the basic concepts go back to poincare the main thrust of chapters i and ii is to explain rather discursively some of received by the editors december 14 1983 1980 mathematics subject classification primary 00a25 00a99 01a45 01a55 01a60 34a40 34c35 34d10 34d30 35b05 35b35 35b40 35b50 35b30 35k55 54h20 58f25 58f40 58f12 58f10 58d25 58d07 46a40 46e10 47h07 47h20 92a15 92a17 secondary 06f30 35b65 58f13 35j60 46e05 92 03 90 03 90a16 supported in part by national science foundation and institute for advanced study 1984 american mathematical society 0273 0979 84 1 00 25 per page

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

dissipativity theory for nonnegative and compartmental dynamical systems with time delay nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous however in many engineering and life science systems transfers between compartments are not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments including some information of past system states in the system model leads to infinite dimensional delay nonnegative dynamical systems in this note we develop dissipativity theory for nonnegative dynamical systems with time delay using linear storage functionals with linear supply rates these results are then used to develop general stability criteria for feedback interconnections of nonnegative dynamical systems with time delay

global analysis of new malaria intrahost models with a competitive exclusion principle in this paper we propose a malaria within host model with k classes of age for the parasitized red blood cells and n strains for the parasite we provide a global analysis for this model a competitive exclusion principle holds if mathcal r 0 the basic reproduction number satisfies mathcal r 0 leq 1 then the disease free equilibrium is globally asymptotically stable on the contrary if mathcal r 0 1 then generically there is a unique endemic equilibrium which corresponds to the endemic stabilization of the most virulent parasite strain and to the extinction of all the other parasites strains we prove that this equilibrium is globally asymptotically stable on the positive orthant if a mild sufficient condition is satisfied

localization of andre quillen goodwillie towers and the periodic homology of infinite loopspaces abstract let k n be the n th morava k theory at a prime p and let t n be the telescope of a v n self map of a finite complex of type n in this paper we study the k n homology of x the 0th space of a spectrum x and many related matters we give a sampling of our results let p x be the free commutative s algebra generated by x it is weakly equivalent to the wedge of all the extended powers of x we construct a natural map s n x l t n p x l t n x of commutative algebras over the localized sphere spectrum l t n s the induced map of commutative cocommutative k n hopf algebras s n x k n p x k n x satisfies the following properties it is always monic it is an isomorphism if x is n connected n 1 x is torsion and t i x 0 for 1 i n 1 it is an isomorphism only if k i x 0 for 1 i n 1 it is universal the domain of s n x preserves k n isomorphisms and if f is any functor preserving k n isomorphisms then any natural transformation f x k n x factors uniquely through s n x the construction of our natural transformation uses the telescopic functors constructed and studied previously by bousfield and the author and thus depends heavily on the nilpotence theorem of devanitz hopkins and smith our proof that s n x is always monic uses topological andre quillen homology and goodwillie calculus in nonconnective settings

positive linear observers for linear compartmental systems linear compartmental systems are mathematical systems that are frequently used in biology and mathematics the inputs states and outputs of such systems are positive because they denote amounts or concentrations of material for linear dynamic systems the observer problem has been solved the purpose of the observer problem is to determine a linear observer such that the state can be approximated the difference between the state and its estimate should converge to zero the interpretation in terms of a physical system requires that an estimate of the state be positive like the state itself in this paper conditions on the system matrices are presented that guarantee that there exists a positive linear observer such that both the error converges to zero and the estimate is positive

sontag s input to state stability condition and global stabilization using state detection this paper deals with the global stabilization problem for nonlinear system using state detection sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included these conditions are based to a version of a lyapunov like condition proposed by sontag which guarantees input to state stability

a contractive approach to separable lyapunov functions for monotone systems abstract monotone systems preserve a partial ordering of states along system trajectories and are often amenable to separable lyapunov functions that are either the sum or the maximum of a collection of functions of a scalar argument in this paper we consider constructing separable lyapunov functions for monotone systems that are also contractive that is the distance between any pair of trajectories exponentially decreases we assume the system evolves in a forward invariant rectangular domain and the distance between trajectories is defined in terms of a finsler type metric characterized by a possibly state dependent norm when this norm is a weighted one norm we obtain conditions which lead to sum separable lyapunov functions and when this norm is a weighted infinity norm symmetric conditions lead to max separable lyapunov functions in addition we consider two classes of lyapunov functions the first class is separable along the system s state and the second class is separable along components of the system s vector field the latter case is advantageous for many practically motivated systems for which it is difficult to measure the system s state but easier to measure the system s velocity or rate of change