eventual practical stability of impulsive differential equations with time delay in terms of two measurements in this paper we introduce a new stability eventual practical stability for impulsive differential equations with time delay by using lyapunov functions and comparison principle we will get some criteria of eventual practical stability eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements

nonresonance impulsive functional differential inclusions with variable times in this paper we investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions with variable moments the proofs make use of the martelli fixed point theorem for condensing multivalued maps

reachability observability and realizability of continuous time positive systems this paper discusses reachability observability and realizability of single input single output linear time invariant systems in which state variables and or input output functions are restricted to be nonnegative to reflect physical constraints frequently encountered in real systems we define a set reachable from the origin with nonnegative inputs and also a set observable with nonnegative outputs we investigate geometrical structures of the sets through convex analysis and a duality relation between them is established next we consider positive realization of a given transfer function using the reachable set and the observable set we give a necessary and sufficient condition for positive realizability an example is given to demonstrate that a positive realizable transfer function does not in general have a jointly controllable and observable positive realization

towards a language theory for infinite n free pomsets n free or series parallel pomsets are a model for the behavior of modularly constructed concurrent systems the investigation of recognizable languages of finite n free pomsets was initiated by lodaya and weil who extended the theorems by kleene and by myhill and nerode on recognizable word languages to this setting in this paper we extend lodaya and weil s results in several aspects a we consider the relation of recognizable sets to monadic second order logic in order to generalize buchi s theorem b we prove our results and extensions of results by lodaya and weil for sets of infinite n free pomsets and c we investigate first order axiomatizable starfree and aperiodic sets of infinite n free pomsets and prove results in the spirit of mcnaughton and papert s and schutzenberger s theorems for finite words

uniform boundedness and stability criteria in terms of two measures for impulsive integro differential equations1research supported by nserc canada 1 this paper establishes several criteria on uniform boundedness and stability in terms of two measures for impulsive integro differential equations by the method of lyapunov functions the interplay of two different measures and the discontinuities of solutions create additional difficulties in choosing suitable minimal set of functions along which the derivative of the lyapunov function is estimated consequently very complicated analysis is required in the proof of the theorems

regular languages defined with generalized quantifiers we study an extension of first order logic obtained by adjoining quantifiers that count with respect to an integer modulus it is shown that the languages definable in this framework are precisely the regular languages whose syntactic monoids contain only solvable groups we obtain an analogous result for regular languages and establish some connections with complexity theory for fixed depth families of circuits

an extension of kleene s and ochman ski s theorems to infinite traces abstract as was noted by mazurkiewicz traces constitute a convenient tool for describing finite behaviour of concurrent systems extending in a natural way mazurkiewicz s original definition infinite traces have recently been introduced enabling one to deal with infinite behaviour of nonterminating concurrent systems in this paper we examine the basic families of recognizable sets and of rational sets of infinite traces the seminal kleene characterization of recognizable subsets of the free monoid and its subsequent extensions to infinite words due to buchi and to finite traces due to ochmanski are the cornerstones of the corresponding theories the main result of our paper is an extension of these characterizations to the domain of infinite traces using recognizing and weakly recognizing morphisms as well as a generalization of the schutzenberger product of monoids we prove various closure properties of recognizable trace languages moreover we establish normal form representations for recognizable and rational sets of infinite traces

necessary conditions for positive realizability of continuous time linear systems abstract this paper deals with the positive realization problem the problem is to find from a given transfer function a state equation in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative necessary conditions are investigated and a new one is given together with some related results

on the reduction principle for differential equations with piecewise constant argument of generalized type abstract in this paper we introduce a new type of differential equations with piecewise constant argument epcag more general than epca k l cooke j wiener retarded differential equations with piecewise constant delays j math anal appl 99 1984 265 297 j wiener generalized solutions of functional differential equations world scientific singapore 1993 the reduction principle v a pliss the reduction principle in the theory of the stability of motion izv akad nauk sssr ser mat 27 1964 1297 1324 in russian v a pliss integral sets of periodic systems of differential equations nauka moskow 1977 in russian is proved for epcag the structure of the set of solutions is specified we establish also the existence of global integral manifolds of quasilinear epcag in the so called critical case and investigate the stability of the zero solution

positive nonlinear realizations of response maps abstract the problem of realization of a positive response map as a positive initialized system on a finite dimensional euclidean state space is investigated the dynamical part of the system is described by a delta differential equation on an arbitrary time scale this incorporates continuous and discrete time systems the main result states necessary and sufficient conditions for existence of positive realization of a particular class the criterion is expressed in the language of skew differential global universes

canonical forms for positive discrete time linear control systems abstract in this paper the properties of reachability controllability and essential reachability of positive discrete time linear control systems are studied these properties are characterized in terms of the directed graph of the state matrix from these characterizations canonical forms of those properties are deduced

practical stability of impulsive functional differential equations in terms of two measurements in this paper we consider practical stability of impulsive functional differential equations in terms of two measurements some sufficient conditions of uniform practical stability for functional differential equation with impulses are obtained by using piecewise continuous lyapunov functions and razumikhin techniques an example illustrates the effectiveness of the proposed result

impulsive neutral functional differential equations with variable times abstract in this paper a fixed point theorem due to schaefer is used to investigate the existence of solutions for first and second order impulsive neutral functional differential equations with variable times

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

positive realizations of linear systems abstract this paper deals with the realization problem of linear systems in which a sign pattern is imposed on the realization a b c t this problem arises in the context of positive linear systems i e systems in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative using a unitary framework for continuous time and discrete time systems we derive necessary and sufficient conditions for positive realizability by means of convex analysis moreover the complete solution in the case of a transfer function of mcmillan degree n 3 is obtained

a new comparison principle for impulsive differential systems with variable impulsive perturbations and stability theory in this paper the stability properties in terms of two measures for impulsive differential systems with variable impulses are investigated a new comparison principlem which allows trajectories strike the same hypersurface finite times is established and then be applied to obtain a stability criterion finally one example is worked out to show the advantage of our results

about new analogies of gronwall bellman bihari type inequalities for discontinuous functions and estimated solutions for impulsive differential systems abstract in this article we present new integral gronwall bellman bihari type inequalities for discontinuous functions integro sum inequalities as applications we investigate estimated solutions for impulsive differential systems conditions of boundedness stability practical stability

on syntactic congruences for ω languages for languages several notions of syntactic congruence were defined the present paper investigates relationships between the so called simple because it is a simple translation from the usual definition in the case of finitary languages syntactic congruence and its infinitary refinements investigated by arnold ar85 we show that in both cases not every language having a finite syntactic monoid is regular and we give a characterization of those languages having finite syntactic monoids as the main result we derive a condition which guarantees that the simple syntactic congruence and arnold s syntactic congruence coincide and show that all languages in the borel class f g satisfy this condition finally we define an alternative canonical object for languages namely a family of right congruence relations using this object we give a necessary and sufficient condition for a regular language to be accepted by its minimalstate automaton

on quasi stability for impulsive differential systems on developpe une theorie de la stabilite relativement a une solution donnee de systemes differentiels impulsifs une telle etude conduit a un mecanisme complique et les notions de stabilite doivent etre modifiees

on the existence of a positive realization the positive realization problem for linear systems is to find conditions for a given transfer function with nonnegative impulse response to have a realization such that the resulting system is a positive system recently it has been shown that under a mild assumption on the long term behaviour of the impulse response this problem is related to the maximum modulus poles only in this paper necessary and sufficient conditions for positive realizability of discrete time systems are given they show that also nondominant poles play a role in the most general case positive realizability conditions for the continuous time case are also given

nonoscillation and positivity of solutions to first order state dependent differential equations with impulses in variable moments abstract the state dependent delay differential equation x t i 1 m p i t x t h i x t f t t 0 x 0 with state dependent impulses is under consideration sufficient conditions for positivity of solutions to the cauchy and periodic problems as well as conditions for positivity of solutions to the problem with a condition on the right end of the interval 0 are given sufficient conditions for nonoscillation of solutions to the homogeneous equation f 0 0 on the half line are formulated

characterizations of rational ω languages by means of right congruences abstract by means of right congruences we characterize in a unified way different classical classes of rational languages a new congruence associated with an automaton is introduced named cycle congruence the family of rational languages which have by morphism a unique minimal recognizing automaton is characterized it appears that for such a minimal automaton the cycle congruence coincides with the syntactic congruence of the recognized language we prove that the other rational languages have an infinite number of minimal automaton

impulsive functional differential equations with variable times in this note a schaefer fixed point theorem is used to investigate the existence of solutions for first order impulsive functional differential equations with variable times

the differential equations on time scales through impulsive differential equations in this paper we investigate differential equations on certain tim es cales with transition conditions detc on the basis of reduction to the impulsive differential equations ide detc are in some sense more general than dynamic equations on time scales m bohner a peterson dynamic equations on

bifurcation of three dimensional discontinuous cycles abstract we consider three dimensional discontinuous dynamical systems with non fixed moments of impacts existence of the center manifold is proved for the system the result is applied for the extension of the planar hopf bifurcation theorem m u akhmet perturbations and hopf bifurcation of the planar discontinuous dynamical system nonlinear analysis 60 2005 163 178 illustrative examples are constructed for the theory

non linear impulsive dynamical systems part i stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for non linear impulsive dynamical systems furthermore we generalize dissipativity theory to non linear dynamical systems with impulsive effects specifically the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy dissipated energy over the continuous time system dynamics and dissipated energy over the resetting instants furthermore extended kalman yakubovich popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived finally the framework is specialized to passive and non expansive impulsive systems to provide a generalization of the classical notions of passivity and non expansivity for non linear impulsive systems these results are used in the second part of this paper to develop extensions of the small gain and p

new results on pulse phenomena for impulsive differential systems with variable moments abstract consider the impulsive differential systems with variable moments x f t x t k x x t 0 x 0 t 0 0 x i k x t k x some sufficient conditions that guarantee the absence or presence of pulse phenomena are obtained our results in this paper generalize and improve several known results

on the stability of invariant sets of systems with impulse effect abstract a system of differential equations with impulse effect is considered it is assumed that this system has an invariant set m by means of the direct lyapunov method the necessary and sufficient conditions of its uniform asymptotic stability are obtained the conditions on the perturbations of right hand sides of differential equations and impulse effects under which the uniform asymptotic stability of the invariant set m of the nonperturbed system implies the uniform asymptotic stability of the invariant set of the perturbed system are obtained the stability properties of invariant sets of periodic systems are also studied

periodic boundary value problem for first order differential equations with impulses at variable times in this paper we show the validity of the method of upper and lower solutions to obtain an existence result for a periodic boundary value problem of first order impulsive differential equations at variable times

on generators of rational ω power languages un language parfait est un langage l de la forme l r ou r est un langage de mots finis appele generateur de l etant donne un langage rationel r nous etudions la relation d inclusion dans la famille des generateurs de r 1 1 nous montrons d abord que les generateurs maximaux pour l inclusion sont rationnels constructibles et en nombre fini de plus tout generateur de r est inclus dans l un d entre eux 2 2 nous montrons ensuite que l on peut tester si un generateur est minimal pour l inclusion an power language is an language l of the form l r for some language r called generator of l for a given rational language r we study the relation of inclusion in the family of the generators of r 1 1 we first prove that the maximal generators with respect to the inclusion are rational constructible and finite in number moreover any generator of r is included in one of them 2 2 then we prove that one can test whether a generator is minimal for the inclusion

a syntactic congruence for rational ω languages buchi has proved that if l is a rational language then there exists a finite congruence for which l is saturated in the following sense u v l 0 u v l here we define the syntactic congruence of l which is the largest congruence having this property

a combinatorial approach to the theory of ω automata a combinatorial lemma is proved and used here to derive new results on automata and to give simpler proofs of known ones in particular we reprove mcnaughton s fundamental theorem characterizing the regular sequence sets without having to construct a sophisticated automaton the theorem is obtained by coding the behaviour of automata in a second order language and a simple application of the lemma in close analogy now referring to a first order language a theory of counter free automata is developed it is shown that these automata are appropriate for characterizing the star free sequence sets finally the lemma is applied in mathematical logic here new normal form theorems and also decidability results are proved for the first order and the monadic second order theory of certain structures over the ordering of natural numbers

syntactic study of recognizable parts of infinite words resume cet article est le deuxieme volet d une etude concernant l extension de la theorie des varietes de eilenberg aux mots infinis a chaque variete de semigroupes v on associe trois classes de parties reconnaissables de mots infinis v v et v s les deux premieres liees a la nature des automates ont fait l object d une etude anterieure le present article est consacre a la classe v s nous montrons qu elle est liee a la syntaxe des parties est decidable avec v et peut se preter a d agreables descriptions comme dans le cas des parties localement testables ou testables par morceaux

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

generalized automata on infinite trees and muller mcnaughton s theorem abstract we introduce various types of top down and bottom up generalized automata on infinite trees we study the power of deterministic and nondeterministic generalized tree automata and prove that deterministic and nondeterministic bottom up automata accept the same class we prove also that nondeterministic top down and bottom up generalized automata have the same power we give various characterizations of the monadic second order theory of the tree in terms of tree automata and tree grammars we consider different types of extensions of muller mcnaughton s theorem but unfortunately not all the extensions of it are possible

a class of differential equations with impulses at variable times on banach spaces abstract in this paper two typical classes of semilinear evolution equation with impulses at variable times on infinite dimensional spaces are considered introducing the reasonable pc mild solutions we discuss the local existence maximal existence interval global existence of pc mild solution for two models in addition to the pulse phenomena an example is given for demonstration

some new integral inequalities of bellman bihari type with delay for discontinuous functions abstract in this article we investigate some integral functional inequalities of bellman bihari type for piecewise continuous functions with some fixed points of discontinuity we also prove a new analogy and generalization of results which were obtained by bellman and bihari to integro sum inequalities with delay and discontinuities that do not belong to lipschitz s type

infinite word languages and continuous mappings abstract languages with infinite words have often been studied as subsets of a topological space the topology used for this purpose was always the natural topology of sequences this paper suggests that another topology may be more useful it is obtained by taking lim w as the derived set of w the resulting topological space is shown to be completely regular strongly zero dimensional and not normal the languages appearing in the theory of automata are shown to be closely related to functionally closed sets continuous inverse images of the set 0 as a consequence a number of known results can be expressed and proved in terms of continuous mappings

various hierarchies of wω regular sets barua 1992 studied a hierarchy rn n 1 2 3 where rn is a class of regular sets which are decomposed into n rational g sets forming a decreasing sequence on the other hand kaminski 1985 defined a hierarchy bm m 1 2 3 where bm is a class of regular sets which are decomposed into 2m rational g sets not necessarily forming a decreasing sequence we prove that r2n bn in spite of the difference of defining conditions

learning regular omega languages we provide an algorithm for learning an unknown regular set of infinite words using membership and equivalence queries three variations of the algorithm learn three different canonical representations of omega regular languages using the notion of families of dfas one is of size similar to l a dfa representation recently learned using l 7 the second is based on the syntactic forc introduced in 14 the third is introduced herein we show that the second can be exponentially smaller than the first and the third is at most as large as the first two with up to a quadratic saving with respect to the second

pulse phenomena of second order impulsive differential equations with variable moments abstract this paper obtains sufficient conditions for presence or absence of pulse phenomena of second order impulsive differential equations with variable times

pulse accumulation in impulsive differential equations with variable times abstract we study pulse accumulation phenomena in first order impulsive differential equations and give necessary and sufficient conditions to ensure pulse accumulation in such equations

perturbations and hopf bifurcation of the planar discontinuous dynamical system abstract the objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point a new technique of investigation is presented conditions for existence of the foci and centres are proposed the focus centre problem and hopf bifurcation are considered appropriate examples are given to ilustrate the bifurcation theorem

a list of arithmetical structures complete with respect to the first order definability a structure with base set n is complete with respect to the first order definability in the class of arithmetical structures if and only if the operations are definable in it a list of such structures is presented although structures with pascal s triangles modulo n are preferred a little an effort was made to collect as many simply formulated results as possible

on projective and separable properties a language l over the cartesian product of component alphabets is called projective if it is closed under projections that is together with each word e l it contains all the words that have the same projections up to stuttering as we prove that in each of the behavior classes regular regular and star free regular i e definable by linear temporal logic languages the projective languages are precisely the boolean combinations of stuttering closed component languages from the corresponding class languages of these behavior classes can also be seen as properties of various temporal logics some uses of projective properties for specification and verification of programs are studied

a constructive approach to boundary value problems with state dependent impulses we investigate the non linear system of ordinary differential equations u t f t u t a e t a b subject to the state dependent impulse condition u t u t u t for t a b such that g t u t 0 and the linear two point boundary condition a u a c u b d here a b f and are given continuous vector functions g is a continuous scalar function a c are constant matrices and d is a constant vector the instants of time t where the jump occurs are determined by the equation g t u t 0 and thus are unknown a priori and essentially depend on the solution u we discuss a reduction technique allowing one to combine the analysis of existence of solutions with an efficient construction of approximate solutions at present according to the authors knowledge no numerical results for boundary value problems with state dependent impulses are available in the literature

well quasi orders and regular ω languages in on regularity of context free languages theoret comput sci 27 1983 311 ehrenfeucht et al showed that a set l of finite words is regular if and only if l is closed under some monotone well quasi order wqo over finite words we extend this result to regular languages that is 1 an language l is regular if and only if l is closed under a periodic extension of some monotone wqo over finite words and 2 an language l is regular if and only if l is closed under a wqo over words that is a continuous extension of some monotone wqo over finite words

about a generalization of bellman bihari type inequalities for discontinuous functions and their applications abstract in the present paper we introduce the conditions of solvability for chaplygin s problem with discontinuous functions in two independent variables satisfying integro sum inequalities the new type of nonlinear integral and wendroff s inequality for discontinuous functions are investigated as applications the conditions of boundedness solutions of partial differential equations of hyperbolic type with impulse influence on some hypersurfaces j r 2 are obtained some historical aspects of the theory of integro sum inequalities are presented

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems

a hierarchy of sets of infinite trees a hierarchy of sets of infinite valued trees is introduced which has no counterpart in the theory of sets of infinite strings languages as a consequence we obtain that for sets of infinite trees an analogue of mcnaughton s fundamental theorem on languages does not hold