existence of solutions for integral inclusions this paper presents sufficient conditions for the existence of solutions to a nonlinear integral inclusion being a volterra counterpart of an integral inclusion arising in traffic theory our results are obtained via a martelli type fixed point theorem and lead to new existence principles

necessary and sufficient small gain conditions for integral input to state stable systems a lyapunov perspective this paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input to state stable iiss systems with external inputs the treatment of iiss and input to state stable iss systems is unified both necessary conditions and sufficient conditions are investigated using a lyapunov formulation in the presence of model uncertainty this paper proves that for the stability of the interconnected system at least one subsystem is necessarily iss which is a stronger stability property in the set of iiss the necessity of a small gain type property is also demonstrated this paper proposes a common form of smooth lyapunov functions which can establish the iiss and the iss of the interconnection comprising iiss and iss subsystems whenever the small gain type condition is satisfied the result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature global asymptotic stability is discussed as a special case

geometrical phase in the cyclic evolution of non hermitian systems the authors derive by a biorthonormal state approach the analogy of berry s phase factor for open non conservative systems for both adiabatic and non adiabatic evolution in the latter case a non unitary evolution operator method is exploited an application is given to the optical supermode propagation in the free electron laser

semilinear differential inclusions via weak topologies abstract the paper deals with the multivalued initial value problem x a t x x f t x for a a t a b x a x 0 in a separable reflexive banach space e the nonlinearity f is weakly upper semicontinuous in x and the investigation includes the case when both a and f have a superlinear growth in x we prove the existence of local and global classical solutions in the sobolev space w 1 p a b e with 1 p introducing a suitably defined lyapunov like function we are able to investigate the topological structure of the solution set our main tool is a continuation principle in frechet spaces and we prove the required pushing condition in two different ways some examples complete the discussion

integral input to state stable systems in cascade the integral input to state stability iiss property is studied in the context of nonlinear time invariant systems in cascade some sufficient conditions for the preservation of the iiss property under a cascade interconnection are presented these are first given as growth restrictions on the supply functions of the storage function associated with each subsystem and are then expressed as solutions based requirements a lyapunov based condition guaranteeing that the cascade composed of an iiss system driven by a globally asymptotically stable gas one remains gas is also provided we also show that some of these results extend to cascades composed of more than two subsystems

nonlinear boundary value problems for multivalued differential equations in banach spaces with f j x x 0 xmultivalued map j a b compact real interval x banach space a t x is a continuous operator on x for each t x e j x x l c j x x is a linear continuous operator from the space of all continuous functions x j x whose range is contained in x h c j x x is a continuous operator nonlinear in general such problems have been studied repeatedly in the literature with different hypotheses on a f l h the pioneering work with conditions similar to the ones used in the present paper but for ordinary differential equations is the note by scrucca l where the operator a was independent from the state variable x e x anichini 2 has studied analogous problems in the context of ordinary differential systems in ir in which the operator a also depends on x e ir in the case of multivalued differential systems kartsatos 3 has also considered boundary value problems for v valued differential equations but over an unbounded time interval zecca and zezza 4 have extended the work of kartsatos to differential equations in banach spaces in both 3 and 4 the operator a is dependent only on t e j recently papageorgiu 5 has established the existence of mild solutions on a compact interval with the operator a depending only on t e j but in general is unbounded the fundamental tools used in the existence proofs of all above mentioned works are essentially fixed point theorems schauder s theorem in 11 eilenberg montgomery s theorem in 2 ky fan s theorem in 3 4 5 here we use a fixed point theorem due to martelli 6 the idea of the present paper has originated from the study of an analogous problem examined by anichini and conti 7 for ordinary differential systems in m and carbone et al 8 for multivalued differential systems again in ir

on quadratic integral equations in orlicz spaces abstract in this paper we study the quadratic integral equation of the form x t g t x t a b k t s f s x s d s several existence theorems for a e monotonic solutions in orlicz spaces are proved for strongly nonlinear functions f the presented method of the proof can be easily extended to different classes of solutions

two point b v p for multivalued equations with weakly regular r h s abstract a two point boundary value problem associated to a semilinear multivalued evolution equation is investigated in reflexive and separable banach spaces to this aim an original method is proposed based on the use of weak topologies and on a suitable continuation principle in frechet spaces lyapunov like functions are introduced for proving the required transversality condition the linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one some applications are given to the study of periodic and floquet boundary value problems of partial integro differential equations and inclusions appearing in dispersal population models comparisons are included with recent related achievements

common fixed point theorems for some new generalized contractive type mappings in this paper some new generalized contractive type conditions for a pair of mappings in metric space are defined some common fixed point results for these mappings are presented

multiple positive solutions for a class of integral inclusions this paper deals with sufficient conditions for the existence of at least two positive solutions for a class of integral inclusions arising in the traffic theory to show our main results we apply a norm type expansion and compression fixed point theorem for multivalued map due to agarwal and o regan a note on the existence of multiple fixed points for multivalued maps with applications j differential equation 160 2000 389 403

on some measures of noncompactness in the frechet spaces of continuous functions abstract in this paper the frechet spaces of continuous functions defined on a bounded or an unbounded interval with values in the space of all real sequences are considered for those frechet spaces new regular measures of noncompactness are constructed and several properties of these measures are established the results obtained are further applied to infinite systems of functional integral equations

logarithmic perturbation theory for quasinormal modes logarithmic perturbation theory lpt is developed and applied to quasinormal modes qnms in open systems qnms often do not form a complete set so lpt is especially convenient because summation over a complete set of unperturbed states is not required attention is paid to potentials with exponential tails and the example of a poschl teller potential is briefly discussed a numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with qnms

observers to the aid of strictification of lyapunov functions abstract we present a procedure for modifying a weak lyapunov function v into a strict one for this we augment the given function with an auxiliary function v a obtained as a lyapunov function associated with the error dynamics given by an observer designed for the system with the derivative of v as an output function

a small gain condition for interconnections of iss systems with mixed iss characterizations we consider interconnected nonlinear systems with external inputs where each of the subsystems is assumed to be input to state stable iss sufficient conditions of small gain type are provided guaranteeing that the interconnection is iss with respect to the external input to this end we extend recently obtained small gain theorems to a more general type of interconnections the small gain theorem provided here is applicable to situations where the iss conditions are formulated differently for each subsystem and are either given in the maximization or the summation sense furthermore it is shown that the conditions are compatible in the sense that it is always possible to transform sum formulations to maximum formulations without destroying a given small gain condition an example shows the advantages of our results in comparison with the known ones

attractivity for functional volterra integral equations of convolution type in this paper we investigate the existence of attractive and uniformly locally attractive solutions for a functional nonlinear integral equation with a general kernel we use methods and techniques of fixed point theorems and properties of measure of noncompactness we extend and generalize results obtained by other authors in the context of fractional functional differential equations

two component eigenfunction expansion for open systems described by the wave equation i completeness of expansion the concept of eigenfunction expansions for the wave equation is generalized to open systems in which waves escape to the outside these non conservative systems are non hermitian in the usual sense it is shown that the natural framework is an eigenfunction expansion within a two component formalism that treats the wavefunction and its conjugate momentum together provided the system approaches spatial infinity rapidly without tails and possesses spatial discontinuities the expansion in terms of the eigenfunctions which are now quasinormal modes is shown to be valid

a small gain theorem in the absence of strong iiss previous small gain results for interconnected integral input to state iiss systems have been restricted to systems that are strongly iiss this paper removes this restriction by allowing cross terms between external inputs and states in the lyapunov decrease of component systems and subsequently constructing a nonseparable lyapunov function an example demonstrates the use of this new small gain formulation

on the attractivity of solutions for a class of multi term fractional functional differential equations in this paper we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations in our consideration we apply the well known schauder fixed point theorem in conjunction with the technique of measure of noncompactness moreover we provide some examples to illustrate the effectiveness of the obtained results

a tight small gain theorem for not necessarily iss systems a new version of the small gain theorem is presented for nonlinear finite dimensional systems the result provides conditions for global asymptotic stability under relaxed assumptions in particular the two interconnected subsystems need not be input to state stable in open loop

lyapunov formulation of iss cyclic small gain in continuous time dynamical networks this paper provides a lyapunov formulation of the cyclic small gain theorem for general dynamical networks large scale systems composed of continuous time input to state stable iss subsystems iss lyapunov functions for continuous time dynamical networks satisfying cyclic small gain conditions are constructed from the iss lyapunov functions of the subsystems

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

two component eigenfunction expansion for open systems described by the wave equation ii linear space structure for a broad class of open systems described by the wave equation the eigenfunctions which are quasinormal modes provide a complete basis for simultaneously expanding outgoing wavefunctions in this paper the linear space structure associated with this expansion is developed under a modified inner product the time evolution operator is self adjoint even though energy is not conserved for the system alone thus the eigenfunctions are mutually orthogonal consequently the usual tools of eigenfunction expansions can be transcribed to these open systems as an example the time independent perturbation theory is developed in straightforward analogy with quantum mechanics giving the shift in both the real part and the imaginary part of the eigenvalues

a note on the existence of multiple fixed points for multivalued maps with applications abstract in this paper we discuss the existence of multiple fixed points for multivalued maps our fixed point results automatically lead to new existence principles for integral inclusions

fractional order integral equations of two independent variables in this paper we present some results concerning the existence the uniqueness and the attractivity of solutions for some functional integral equations of riemann liouville fractional order by using some fixed point theorems

existence and uniqueness of common fixed points for two multivalued operators in ordered metric spaces in this paper we discuss some new fixed point theorems for a pair of multivalued operators which satisfy weakly generalized contractive conditions our results are the extension and improvement of corresponding results of j harjani and k sadarangani fixed point theorems for weakly contractive mappings in partially ordered sets nonlinear analysis 71 2009 3403 3410 and x zhang common fixed point theorems for some new generalized contractive type mappings j math anal appl 333 2007 780 786 finally some examples are given to illustrate the usability of our results

positive solutions of fourth order boundary value problems with two parameters abstract in this paper the existence results of positive solutions are obtained for fourth order boundary value problem u 4 u u f t u 0 where f 0 1 r r is continuous r and satisfy

hybrid fixed point theory for strictly monotone increasing multi valued mappings with applications in this paper a general hybrid fixed point theorem for the strict monotone increasing multi valued mappings in ordered banach spaces is proved via measure of noncompactness and it is further applied to perturbed functional nonconvex differential inclusions for proving the existence results for the extremal solutions under mixed lipschitz compactness and strict monotonic conditions

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

study on existence of solutions for some nonlinear functional integral equations abstract using the technique of measures of noncompactness in banach algebra we employ abstract fixed point theorems such as darbo s theorem to study the existence solution in banach algebra c 0 a for some functional integral equations which include many key integral and functional equations that arise in nonlinear analysis

investigation on the existence of solutions for some nonlinear functional integral equations abstract we prove an existence theorem for a nonlinear integral equation which is a volterra counterpart of an integral equation arising in traffic theory using the technique of the measure of noncompactness in banach algebra we prove an existence theorem for a nonlinear functional integral equation basic fixed point theorems such as darbo s theorem are employed to obtain the aforementioned aims in banach algebra

hybrid fixed points of multivalued operators in metric spaces with applications abstract this paper deals with the existence of hybrid fixed points involving two multivalued operators in a complete metric space our claim is also illustrated with applications to a class of integral inclusions for proving the existence results

application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution abstract the aim of this article is to investigate the existence of solution for the nonlinear functional integral equations with the help of measure of noncompactness simulation function and generalized darbo fixed point theorem also we provided example for the applicability of obtained results to the theory of integral equations also we introduce an iteration algorithm by modified homotopy perturbation and adomian decomposition method to find solution of the above problem with high accuracy finally we have a discussion about convergence and upper bound of error

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

small gain theorems for large scale systems and construction of iss lyapunov functions we consider interconnections of n nonlinear subsystems in the input to state stability iss framework for each subsystem an iss lyapunov function is given that treats the other subsystems as independent inputs a gain matrix is used to encode the mutual dependencies of the systems in the network under a small gain assumption on the monotone operator induced by the gain matrix a locally lipschitz continuous iss lyapunov function is obtained constructively for the entire network by appropriately scaling the individual lyapunov functions for the subsystems the results are obtained in a general formulation of iss the cases of summation maximization and separation with respect to external gains are obtained as corollaries

on existence and asymptotic stability of solutions of a nonlinear integral equation we prove an existence theorem for a nonlinear integral equation being a volterra counterpart of an integral equation arising in the traffic theory the method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question

asymptotic stability equals exponential stability and iss equals finite energy gain if you twist your eyes in this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables the same is shown for input to state stability and input to state exponential stability and for input to state exponential stability and a nonlinear h estimate

on the solution of a nonlinear integral equation on the basis of a fixed point technique and cubic b spline scaling functions in this paper we apply the fixed point method to solve some nonlinear functional volterra integral equations which appear in many physical chemical and biological problems in each iteration of this method cubic semi orthogonal compactly supported b spline wavelets are used as basis functions to approximate the solution also the convergence of this numerical method is investigated and some examples are presented to show the accuracy and convergence of the method

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

strict lyapunov function constructions under lasalle conditions with an application to lotka volterra systems we provide new techniques for building explicit global strict lyapunov functions for broad classes of periodic time varying nonlinear systems satisfying lasalle conditions we illustrate our work using the lotka volterra model which plays a fundamental role in bioengineering we use our strict lyapunov constructions to prove robustness of the lotka volterra tracking dynamics to uncertainty in the death rates

on local attractivity and asymptotic stability of solutions of a quadratic volterra integral equation the existence of solutions of a nonlinear quadratic volterra integral equation is studied in our considerations we apply the technique of measures of noncompactness in conjunction with the classical schauder fixed point principle such an approach allows us to obtain a result on the existence of solutions of an equation in question which are uniformly locally attractive or asymptotically stable

existence of positive solutions for a second order ordinary differential system abstract in this paper we consider the existence of positive solutions for a second order ordinary differential system where the nonlinear term is superlinear in one equation and sublinear in the other equation by constructing a cone k 1 k 2 which is the cartesian product of two cones in space c 0 1 and computing the fixed point index in k 1 k 2 we establish the existence of positive solutions for the system we remark that differently from the literature we deal with our problem on the cartesian product of two cones in which the feature of two equations can be exploited better

bistable biological systems a characterization through local compact input to state stability many biological systems have the capacity to operate in two distinct modes in a stable manner typically the system can switch from one stable mode to the other in response to a specific external input mathematically these bistable systems are usually described by models that exhibit at least two distinct stable steady states on the other hand to capture biological variability it seems more natural to associate to each stable mode of operation an appropriate invariant set in the state space rather than a single fixed point a general formulation is proposed in this paper which allows freedom in the form of kinetic interactions and is suitable for establishing conditions on the existence of one or more disjoint forward invariant sets for the given system stability with respect to each set is studied in terms of a local notion of input to state stability with respect to compact sets two well known systems that exhibit bistability are analyzed in this framework the lac operon and an apoptosis network for the first example the question of designing an input that drives the system to switch between modes is also considered

fixed points of multivalued operators in ordered metric spaces with applications abstract the purpose of this paper is to present some new hybrid fixed point theorems involving multivalued operators which satisfy weakly generalized contractive conditions in an ordered complete metric space an example of the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is given to illustrate the usability of our results

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

excited bound state logarithmic perturbation theory without nodes the logarithmic perturbation theory is modified slightly in order to deal with excited states instead of considering a real wavefunction describing the physical stationary state the authors consider a complex wavefunction at the same energy by mixing in the ghost state for excited bound states the former has nodes while the latter is guaranteed not to have any nodes and can be represented simply as exp g to which the logarithmic perturbation method can be applied in a straightforward manner the physical entities the energy corrections are independent of the amount of mixing of the ghost state the connection to the green function method is also shown the freedom to mix in the ghost state allows the authors to justify an ad hoc approach whereby the simple version of the logarithmic perturbation theory is applied to excited bound states the formalism is illustrated with simple examples

exponential stability of two dimensional homogeneous monotone systems with bounded directional delays one dimensional 1 d monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties one of these special properties is that for lti monotone systems exponential stability is insensitive to time delays some extensions to 1 d nonlinear monotone systems based on conditions of homogeneity have also been reported in this paper we study the problem of exponential stability of discrete time 2 d nonlinear monotone systems described by the roesser model with time varying delays specifically based on the monotone property and homogeneity of the associated vector fields necessary and sufficient delay independent exponential stability conditions are derived the magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance two examples are given to demonstrate the effectiveness of the obtained results

a lyapunov approach to cascade interconnection of integral input to state stable systems this technical note deals with the stability of cascade interconnection of integral input to state iiss time varying systems a new technique to construct smooth lyapunov functions of cascaded systems is proposed from the construction sufficient conditions for internal stability and stability with respect to external signals are derived one of the derived conditions is a trade off between slower convergence of the driving system and steeper input growth of the driven system the trade off is no more necessary if the speed of convergence of the driven system is not radially vanishing the results are related to trajectory based approaches and small gain techniques for feedback interconnection the difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts

robust stabilization of nonlinear cascaded systems this paper considers the problem of robust stabilization for an uncertain nonlinear system which is a cascaded interconnection of two subsystems both of the subsystems are allowed to be nonlinear multi variable and containing uncertain parameters we present a new approach to designing stabilizing controllers which assure both robust global asymptotic stability and local quadratic stability compared with existing results the assumptions required for such robust stabilizing controllers to exist are significantly simplified

construction of lyapunov functions for interconnected parabolic systems an iiss approach this paper is devoted to two issues the first one is to provide lyapunov based tools to establish integral input to state stability iiss and input to state stability iss for some classes of nonlinear parabolic equations the other one is to provide a stability criterion for interconnections of iiss parabolic systems the results addressing the former problem allow us to overcome obstacles arising in tackling the latter one the results for the latter problem are a small gain condition and a formula of lyapunov functions which can be constructed for interconnections whenever the small gain condition holds it is demonstrated that for interconnections of partial differential equations the choice of a right state and input spaces is crucial in particular for iiss subsystems which are not iss as illustrative examples stability of two highly nonlinear reaction diffusion systems is established by the proposed small gain criterion

on existence and local attractivity of solutions of a quadratic volterra integral equation of fractional order in the paper we study the existence of solutions of a nonlinear quadratic volterra integral equation of fractional order this equation is considered in the banach space of real functions defined continuous and bounded on an unbounded interval moreover we show that solutions of this integral equation are locally attractive

the global attractivity and asymptotic stability of solution of a nonlinear integral equation abstract in this paper we employ the fixed point theorem to study the existence of an integral equation and obtain the global attractivity and asymptotic stability of solutions of the equation some new results are given

fixed point theorems in the frechet space c r and functional integral equations on an unbounded interval abstract the purpose of this paper is to establish fixed point theorems for operators in the frechet space of continuous functions on the real half axis in our considerations we apply the technique of measures of noncompactness in conjunction with the tikchonov fixed point theorem the obtained results are applied in the proof of the solvability of a nonlinear functional integral equation with the initial value moreover we show that solutions of that equation are uniformly globally asymptotically attractive the results presented in the paper allow to improve existence theorems for integral and functional equations obtained earlier in many research papers

construction of lyapunov krasovskii functionals for networks of iiss retarded systems in small gain formulation this paper tackles a problem of verifying stability of retarded dynamical networks in a dissipative formulation subsystems are assumed to be integral input to state stable iiss time delays are allowed to reside in both subsystems and interconnection channels and may be both discrete and distributed no assumption is made on the interconnection topology a small gain methodology is developed for constructing a lyapunov krasovskii functional to establish iiss of such a network

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

a general multi valued hybrid fixed point theorem and perturbed differential inclusions abstract combining three basic multi valued versions of banach schauder and tarski fixed point theorems a general hybrid fixed point theorem for multi valued mappings in banach spaces is proved via measure of noncompactness and it is further applied to perturbed differential inclusions for proving the existence results under mixed lipschitz compactness and monotone conditions

brief growth rate conditions for uniform asymptotic stability of cascaded time varying systems in the last decade several results on cascaded autonomous systems have appeared in the literature the sufficient conditions for the stability and stabilizability of these systems are often related to certain growth rate conditions on the functions which define the dynamics of the system in this paper we analyze three complementary classes of nonlinear time varying systems according to these growth rates for each case we give further results to guarantee uniform global asymptotic stability of the cascade and relate our contributions to input to state stability and other growth rate conditions previously reported the advantage of this type of analysis is that it is often easier to verify such conditions than to find a lyapunov function with a negative definite derivative

existence of nondecreasing solutions of a quadratic integral equation of volterra type nondecreasing solutions of the quadratic integral equations is an interesting subject in the area of mathematics sciences and engineering using the theory of measures of noncompactness and applying a new method we prove the existence of nondecreasing solutions of a quadratic integral equation of volterra type in c i

global stabilization of nonlinear systems based on vector control lyapunov functions this paper studies the use of vector lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems recent results on vector lyapunov functions are utilized the main result of the paper shows that the existence of a vector control lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback applications to nonlinear systems are provided practically checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law the obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor

strong iiss is preserved under cascade interconnection in a recent paper we have introduced the notion of strong iiss as a compromise between the strength of input to state stability iss and the generality of integral iss iiss in this note we continue the investigations around this property by studying its behavior in an interconnection context in particular we show that the cascade of strongly iiss systems is itself strongly iiss and we recall some useful tools to study strongly iiss systems in feedback interconnection

global stabilization of nonlinear cascade systems abstract we present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems these are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section for polynomial systems in particular the stabilizing feedback is given explicitly

an iiss framework for stochastic robustness of interconnected nonlinear systems this paper addresses integral input to state stability iiss for stochastic nonlinear dynamical systems and develops lyapunov type criteria the developments offer an iiss small gain framework for verifying robustness of interconnected systems with respect to disturbances the framework not only includes input to state stability iss as a special case but also highlights fundamental differences between the stochastic and deterministic systems in particular dealing with nonlinearities in interconnection gives rise to a unique issue of degradation in the presence of stochastic noises this paper addresses this issue by coping judiciously with the effect of the gradient of lyapunov functions of subsystems through diffusion fields in composing a lyapunov function of the entire system this paper employs two types of robustness notions and demonstrates that the influence of the stochastic degradation on one notion is considerably different from the influence on the other notion in dealing with interconnected systems

connection between cooperative positive systems and integral input to state stability of large scale systems we consider a class of continuous time cooperative systems evolving on the positive orthant r n we show that if the origin is globally attractive then it is also globally stable and furthermore there exists an unbounded invariant manifold where trajectories strictly decay this leads to a small gain type condition which is sufficient for global asymptotic stability gas of the origin we establish the following connection to large scale interconnections of integral input to state stable iss subsystems if the cooperative system is integral iss and arises as a comparison system associated with a large scale interconnection of i iss systems then the composite nominal system is also i iss we provide a criterion in terms of a lyapunov function for integral input to state stability of the comparison system furthermore we show that if a small gain condition holds then the classes of systems participating in the large scale interconnection are restricted in the sense that certain iiss systems cannot occur moreover this small gain condition is essentially the same as the one obtained previously by dashkovskiy ruffer and wirth 2007 in press for large scale interconnections of iss systems

fixed point method for solving nonlinear quadratic volterra integral equations we consider a paper of banas and sadarangani 2008 11 which deals with monotonicity properties of the superposition operator and their applications an application of the monotonicity properties is to study the solvability of a quadratic volterra integral equation in this paper we prepare an efficient numerical technique based on the fixed point method and quadrature rules to approximate a solution for quadratic volterra integral equation then convergence of numerical scheme is proved by some theorems and some numerical examples are given to show applicability and accuracy of the numerical method and guarantee the theoretical results

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

robust stability of networks of iiss systems construction of sum type lyapunov functions this paper gives a solution to the problem of verifying stability of networks consisting of integral input to state stable iiss subsystems the iiss small gain theorem developed recently has been restricted to interconnections of two subsystems for large scale systems stability criteria relying only on gain type information that were previously developed address only input to state stable iss subsystems to address the stability problem involving iiss subsystems interconnected in general structure this paper shows how to construct lyapunov functions of the network by means of a sum of nonlinearly rescaled individual lyapunov functions of subsystems under an appropriate small gain condition

input to state stability of impulsive stochastic delayed systems under linear assumptions in this paper the input to state stability iss integral iss iiss and stochastic iss siss are investigated for impulsive stochastic delayed systems by means of the lyapunov krasovskii function and the average impulsive interval approach the conditions for iss type properties are derived under linear assumptions respectively for destabilizing and stabilizing impulses it is shown that if the continuous stochastic delayed system is iss and the impulsive effects are destabilizing then the hybrid system is iss with respect to a lower bound of the average impulsive interval moreover it is unveiled that if the continuous stochastic delayed system is not iss the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval an improved comparison principle is developed for impulsive stochastic delayed systems which facilitates the derivations of our results for iss iiss siss an example of networked control systems is provided to illustrate the effectiveness of the proposed results

an application of the continuous selection theorem to the study of the fixed points of multivalued mappings abstract applying the continuous selection theorem given by k przestawski and l rybinski michael selection theorem under weak lower semicontinuity assumption proc amer math soc in press we state the result on continuous dependence of the fixed points of set valued contractions and the krasnoselski type fixed point theorem for multivalued mappings

on a measure of noncompactness in the holder space ck γ ω and its application abstract in this article based on the concept of relative compactness in the holder space c k where k 0 0 1 and is a compact subset of r n we present a new measure of noncompactness on c k moreover as an application we study the existence of solution of a nonlinear integral equation in the holder space by applying darbo fixed point theorem

continuous selections and retractive representations for the fixed points sets of set valued reich s contractions abstract we refine a continuous selection approach adopted earlier to fixed points of set valued banach s contractions an extension of selection and representation results to continuous set valued reich s contractions is given a new krasnoselskii melvin type fixed point theorem is stated as a corollary

existence theory for perturbed impulsive hyperbolic differential inclusions with variable times in this paper the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is proved under the mixed generalized lipschitz and caratheodory s conditions

global output tracking control of a class of euler lagrange systems with monotonic non linearities in the velocities in this paper we address the problem of output feedback tracking control of a class of euler lagrange systems subject to non linear dissipative loads by imposing a monotone damping condition on the non linearities of the unmeasured states the common restriction that the non linearities be globally lipschitz is removed the proposed observer controller scheme renders the origin of the error dynamics uniformly globally asymptotically stable in the general case under certain additional assumptions the result continue to hold for a simplified control law that is less sensitive to noise and unmodelled phenomena

tau approximation method for the weakly singular volterra hammerstein integral equations in this paper we propose a useful method based on the tau method with arbitrary bases to find the numerical solution of weakly singular voletrra hammerstein integral equations in this scheme an operational approach using the orthogonal polynomial bases is presented for converting the problem under consideration to its matrix vector representation error analysis of this method is also presented some numerical examples are provided to illustrate the accuracy and computational efficiency of the method

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

comparison results for initial value problems of second order impulsive integro differential inclusions abstract in this paper we present new maximum and minimum principles for the initial value problem for a class of second order nonlinear impulsive integro differential inclusions with discontinuous multivalued functions on the right hand side in a real banach space this allows us to lead on to the development of the comparison principle and monotone iterative technique for a nonlinear second order impulsive integro differential inclusion