system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

on probabilistic φ contractions on menger spaces abstract recently ciric lj b ciric solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces nonlinear anal 72 2010 2009 2018 obtained a fixed point theorem with the intention to get a probabilistic version of the boyd wong theorem d w boyd j s w wong on nonlinear contractions proc amer math soc 20 1969 458 464 we give a counterexample to the key lemma of ciric and we establish a corrected version of his main theorem we also discuss the relations between our result and fixed point theorems of browder f e browder on the convergence of successive approximations for nonlinear functional equations nederl akad wetensch proc ser a 71 indag math 30 1968 27 35 and matkowski j matkowski integrable solutions of functional equations dissertationes math rozprawy mat 127 1975 68 pp

on boundedness of solutions of state periodic systems a multivariable cell structure approach many dynamical systems are periodic with respect to several state variables this periodicity typically leads to the coexistence of multiple invariant solutions equilibria or limit cycles as a consequence while there are many classical techniques for analysis of boundedness and stability of such systems most of these only permit to establish local properties motivated by this a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented the proposed method is inspired by the cell structure approach developed by leonov and noldus and characterized by two main advances first the conventional cell structure framework is extended to the case of dynamics which are periodic with respect to multiple states second by introducing the notion of a leonov function the usual definiteness requirements of standard lyapunov functions are relaxed to sign indefinite functions furthermore it is shown that under mild additional conditions the existence of a leonov function also ensures input to state stability i e robustness with respect to exogenous perturbations the performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system

on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

backstepping controller synthesis and characterizations of incremental stability incremental stability is a property of dynamical and control systems requiring the uniform asymptotic stability of every trajectory rather than that of an equilibrium point or a particular time varying trajectory similarly to stability lyapunov functions and contraction metrics play important roles in the study of incremental stability in this paper we provide characterizations and descriptions of incremental stability in terms of existence of coordinate invariant notions of incremental lyapunov functions and contraction metrics respectively most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks they can only be applied to control systems in either parametric strict feedback or strict feedback form and they require these control systems to be smooth in this paper we propose a design technique that is applicable to larger classes of control systems including a class of non smooth control systems moreover we propose a recursive way of constructing contraction metrics for smooth control systems and incremental lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems the approximation of stochastic hybrid systems source code model checking for nonlinear dynamical systems and so on the effectiveness of the proposed results in this paper is illustrated by synthesizing controllers rendering two non smooth control systems incrementally stable the first example aims to show how to recursively construct the incremental lyapunov functions the second example aims to show the key role of the computed incremental lyapunov function in constructing a finite abstraction that is equivalent to the system under study

a class of contractions in fuzzy metric spaces using the notion of geometrically convergent t norms a fixed point theorem in fuzzy metric spaces in the sense of kramosil and michalek for a class of contractions larger than the class of e l contraction mappings has been proved

a note on fixed point theorems of hadzci c abstract in this paper we give a fixed point theorem for multi valued probabilistic contraction mappings on a menger space as a special case a fixed point theorem for multi valued contraction mappings on a fuzzy metric space is obtained the results presented improve and generalize in a sense some recent fixed point theorems proved by had ic

model reduction for a class of convergent nonlinear systems in this technical note a model reduction procedure is presented for nonlinear systems that can be decomposed into a feedback interconnection of a linear and nonlinear subsystem conditions for stability of the reduced order model and an error bound are given herein the input to state convergence property is exploited which proves to be useful in the definition and derivation of the error bound the results are illustrated by application to a nonlinear mechanical system

fixed point theorems for nonlinear contractions in kaleva seikkala s type fuzzy metric spaces in this paper the existence and unicity of fixed points for mappings in fuzzy metric spaces in the sense of kaleva and seikkala is discussed nonlinear contractions of the boyd wong s type alber guerre delabriere s type and kannan reich s type are considered and several new fixed point theorems for these contractions in complete fuzzy metric spaces are presented respectively also some error estimates are given for iterations to approximate fixed point previous work with respect to fixed point in fuzzy metric spaces is based on the t conorm max the presented work does away with this restriction by proposing weaker conditions defining a generic class of suitable binary operations as applications the corresponding fixed point theorems for menger probabilistic metric spaces are obtained

a non quadratic criterion for stability of forced oscillations abstract a new test for stability of forced oscillations in nonlinear systems is proposed the result is illustrated by an example of a saturated pi control of an integrator with a harmonic reference signal the range of frequencies and amplitudes that guarantee stability of the corresponding oscillations is found

technical communique uniquely connecting frequency domain representations of given order polynomial wiener hammerstein systems the notion of frequency response functions has been generalized to nonlinear systems in several ways however a relation between different approaches has not yet been established in this paper frequency domain representations for nonlinear systems are uniquely connected for a class of nonlinear systems specifically by means of novel analytical results the generalized frequency response function gfrf and the higher order sinusoidal input describing function hosidf for polynomial wiener hammerstein systems are explicitly related assuming the linear dynamics are known necessary and sufficient conditions for this relation to exist and results on the uniqueness and equivalence of the hosidf and gfrf are provided finally this yields an efficient computational procedure for computing the gfrf from the hosidf and vice versa

synchronization of interconnected systems with applications to biochemical networks an input output approach this paper provides synchronization conditions for networks of nonlinear systems the components of the network referred to as compartments in this paper are made up of an identical interconnection of subsystems each represented as an operator in an extended l2 space and referred to as a species the compartments are in turn coupled through a diffusion like term among the respective species the synchronization conditions are provided by combining the input output properties of the subsystems with information about the structure of the network the paper also explores results for state space models as well as biochemical applications the work is motivated by cellular networks where signaling occurs both internally through interactions of species and externally through intercellular signaling the theory is illustrated by providing synchronization conditions for networks of goodwin oscillators

brief paper diagonal stability of a class of cyclic systems and its connection with the secant criterion we consider a class of systems with a cyclic interconnection structure that arises among other examples in dynamic models for certain biochemical reactions we first show that a secant criterion for local stability derived earlier in the literature is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices we then revisit a recent generalization of this criterion to output strictly passive systems and recover the same stability condition using our diagonal stability result as a tool for constructing a lyapunov function using this procedure for lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties

contraction analysis of nonlinear distributed systems contraction theory is a comparatively recent dynamic analysis and non linear control system design tool based on an exact differential analysis of convergence this paper extends contraction theory to local and global stability analysis of important classes of non linear distributed dynamics such as convection diffusion reaction processes lagrangian and hamilton jacobi dynamics and optimal controllers and observers by contrast with stability proofs based on energy dissipation stability and convergence can be determined for energy based systems excited by time varying inputs the hamilton jacobi bellman controller and a similar optimal non linear observer design are studied based on explicitly computable conditions on the convexity of the cost function these stability conditions extend the well known conditions on controllability and observability grammians for linear time varying systems without requiring the unknown transition matrix of the underlying differential dynamics

an alternative characterization of probabilistic menger spaces with h type triangular norms abstract the class of h type triangular norms was introduced for the first time by had ic in 1978 in this paper a new characteristic property of the h type triangular norm is presented by virtue of this alternative characterization the continuity of quasi metrics and quasi norms is studied and some properties of the probabilistic menger spaces with this triangular norm are considered as applications new fixed point and fixed degree theorems for probabilistic nonlinear contractions and fuzzy mappings are given

on probabilistic φ contractions in menger spaces abstract in this note we show that the fixed point theorems given for menger spaces by j jachymski 2010 5 theorem 1 and j x fang 2015 2 theorem 3 1 are equivalent

on the topological structure of km fuzzy metric spaces and normed spaces in this paper some relations among the axioms of km fuzzy metric spaces and km fuzzy normed spaces are discussed and some characterizations concerning the additional axiom are given also a quasi metric family and a quasi norm family corresponding respectively to the km fuzzy metric spaces and the km fuzzy normed spaces are introduced and studied using their properties the different topological structures of km fuzzy metric spaces and km fuzzy normed spaces with variable t norm are described and some new properties on these spaces are obtained as their special cases the topological structures and properties concerning gv fuzzy metric spaces and gv fuzzy normed spaces are presented

a negative bendixson like criterion for a class of hybrid systems a condition which ensures the absence of periodic orbits for nonsmooth dynamical systems is presented the condition is a higher dimensional generalization of bendixson s criterion applicable to differential inclusions that are useful in the description of hybrid systems the main argument is based on contraction analysis of the d measured volume along the system trajectories a connection to methods for estimating the hausdorff dimension is emphasized for a class of hybrid systems described by a linear system with relay feedback the conditions are presented in the form of linear matrix inequalities a simple but illustrative example is analyzed

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

a contraction approach to the hierarchical analysis and design of networked systems this brief is concerned with the stability of continuous time networked systems using contraction theory a result is established on the network structure and the properties of the individual component subsystems and their couplings to ensure the overall contractivity of the entire network specifically it is shown that a contraction property on a reduced order matrix that quantifies the interconnection structure coupled with contractivity expansion estimates on the individual component subsystems suffices to ensure that trajectories of the overall system converge towards each other

nonlinear contraction theorems in probabilistic spaces abstract in this paper first we prove a common fixed point theorem in menger probabilistic metric spaces then we present a nonlinear contraction case of jungck s common fixed point theorem in menger probabilistic metric spaces finally we prove a common fixed point theorem for six self maps in a menger probabilistic metric space

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

passivity gains and the secant condition for stability a generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems the key is the introduction of a quantity that combines gain and phase information for each system in the cascade for linear one dimensional systems the known result is recovered exactly 2005 elsevier b v all rights reserved

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces abstract the probabilistic version of the classical banach contraction principle was proved in 1972 by sehgal and bharucha reid v m sehgal a t bharucha reid fixed points of contraction mappings on pm spaces math syst theory 6 97 102 their fixed point theorem is further generalized by many authors in the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems however the problem to prove the probabilistic versions of the very important generalization of the banach contraction principle obtained in 1969 by boyd and wong d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 who proved the fixed point theorem for a self mapping of a metric space satisfying the very general nonlinear contractive condition is unsolved in these days similarly as in the metric space case to prove a fixed point theorem for a mapping satisfying the general probabilistic nonlinear contractive condition it was necessary to find a new approach substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition introduced by sehgal and bharucha reid and further used by many authors so the problem to obtain a truthful probabilistic version of the banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years we have solved this problem in this paper

synchronization of goodwin s oscillators under boundedness and nonnegativeness constraints for solutions in the recent paper by hamadeh et al 2012 an elegant analytic criterion for incremental output feedback passivity iofp of cyclic feedback systems cfs has been reported assuming that the constituent subsystems are incrementally output strictly passive iosp this criterion was used to prove that a network of identical cfs can be synchronized under sufficiently strong linear diffusive coupling a very important class of cfs consists of biological oscillators named after brian goodwin and describing self regulated chains of enzymatic reactions where the product of each reaction catalyzes the next reaction while the last product inhibits the first reaction in the chain goodwin s oscillators are used in particular to model the dynamics of genetic circadian pacemakers hormonal cycles and some metabolic pathways in this technical note we point out that for goodwin s oscillators where the individual reactions have nonlinear e g mikhaelis menten kinetics the synchronization criterion obtained by hamadeh et al cannot be directly applied this criterion relies on the implicit assumption of the solution boundedness dictated also by the chemical feasibility the state variables stand for the concentrations of chemicals furthermore to test the synchronization condition one needs to know an explicit bound for a solution which generally cannot be guaranteed under linear coupling at the same time we show that these restrictions can be avoided for a nonlinear synchronization protocol where the control inputs are saturated by a special nonlinear function belonging to a wide class which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them we prove that oscillators synchronize under such a protocol provided that the couplings are sufficiently strong

density dependent cellular growth in an age structured colony abstract the mckendrick von foerster model is often used to model cell colonies with both constant and arbitrarily varying generation times our purpose here is to extend the model by linking the fluctuation of the generation time to the history of the colony such a linkage is natural since for example when a colony grows large enough to severely tax its environment the generation time lengthens accordingly the resulting model consists of a pair of hyperbolic balance laws with a boundary condition of the form u 0 t 2 1 m t u m t t where m depends functionally on the solution u we show the model to be well posed and demonstrate its ability to duplicate observed biological phenomena in a simple case

a note on probabilistic φ contractions in menger spaces abstract in this note we prove that each probabilistic e contraction in a complete menger space x f with of h type is a picard mapping where 0 0 be a function with the properties i 0 1 0 1 ii for each t 0 there exists r t such that lim n n r 0 as a consequence we answer an open question raised by mihet and zaharia affirmatively

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

robust stability analysis of gene protein regulatory networks with cyclic activation repression interconnections abstract this paper investigates analytic robust stability criteria for large scale cyclic gene protein regulatory network systems consisting of genes with heterogeneous dynamics combined with parametric or unstructured uncertainties from a control theoretic viewpoint we first consider a class of gene expressions which is described as an uncertain linear transcription translation model lttm with feedback loops from translation products to transcription next we show that such a model belong to a class of large scale dynamical linear network systems with a generalized frequency variable then we derive robust stability criteria systematically for the following two types of biological uncertain lttm i lttms consisting of heterogeneous gene dynamics with parametric uncertainties and ii lttms consisting of homogeneous nominal gene dynamics with unstructured uncertainties these criteria provide fairly simple analysis methodologies which can be readily applied to the analysis for large scale genetic regulatory networks and give some biological insight

a link between input output stability and lyapunov stability it is shown that incremental boundedness of an input output operator ensures global asymptotic stability of any motion a reciprocal statement is set

some results on exponential synchronization of nonlinear systems based on recent works on transverse exponential stability we establish some necessary and sufficient conditions for the existence of a locally exponential synchronizing control law we show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems on the synchronization manifold by a linear state feedback this in turn is also equivalent to the existence of a symmetric covariant tensor field which satisfies a control matrix function inequality based on this result we provide the construction of such a synchronizer via backstepping approach in some particular cases we show how global exponential synchronization may be obtained

asymptotic amplitudes and cauchy gains a small gain principle and an application to inhibitory biological feedback the notions of asymptotic amplitude for signals and cauchy gain for input output systems and an associated small gain principle are introduced these concepts allow the consideration of systems with multiple and possibly feedback dependent steady states a lyapunov like characterization allows the computation of gains for state space systems and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops an application in biology mapk signaling is worked out in detail

convergence properties for discrete time nonlinear systems three similar convergence notions are considered two of them are the long established notions of convergent dynamics and incremental stability the other is the more recent notion of contraction analysis all three convergence notions require that all solutions of a system converge to each other in this note we investigate the differences between these convergence properties for discrete time and time varying nonlinear systems by comparing the properties in pairs and using examples we also demonstrate a time varying smooth lyapunov function characterization for each of these convergence notions and with appropriate assumptions we provide several sufficient conditions to establish relationships between these properties in terms of lyapunov functions

a note on φ contractions in probabilistic and fuzzy metric spaces abstract in a recent paper fang 2015 1 j x fang generalized a crucial fixed point theorem for probabilistic contractions on complete menger spaces due to jachymski 2010 3 in this note we show that actually fang s theorem is an easy consequence of jachymski s theorem we also observe that the proof of a fixed point theorem for complete metric spaces deduced by fang from his main result is not correct and present a new proof of it

on linearly topological structure and property of fuzzy normed linear space in this paper the simplified definition of fuzzy normed linear space is introduced the different structure of fuzzy normed linear space with variable right norm r is discussed in terms of topological vector space and its properties such as compactness completeness and density are studied under more general left norm l and right norm r as application the linearly topological structure of menger pn space is obtained

delay robustness of interconnected passive systems an integral quadratic constraint approach we consider networks of passive systems with time delays in the interconnections and present a stability analysis technique with the help of the integral quadratic constraint iqc framework unlike the classical passivity approach that fails to characterize delay robustness and the small gain approach that conservatively accounts for arbitrarily large delays the new technique gives sharp stability estimates that depend on the duration of delay since the effect of delay depends on its duration relative to the time scales of the system we make use of a roll off iqc that captures magnitude roll off at high frequencies thus providing the critical time scale information we then combine this roll off iqc with an output strict passivity iqc that incorporates gain and phase information and demonstrate the benefit of this combined iqc approach on a cyclic interconnection structure with delay finally we develop a technique to verify these iqcs for classes of nonlinear state space models and present an example from internet congestion control

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

a generalization of tardiff s fixed point theorem in probabilistic metric spaces and applications to random equations using the infinitely countable extension of triangular norms a generalization of tardiff s fixed point theorem in probabilistic metric spaces is proved as a consequence an application to random equations is obtained ained

on avoiding vertexization of robustness problems the approximate feasibility concept for a large class of robustness problems with uncertain parameter vector q confined to a box q there are many papers providing results along the following lines the desired performance specification is robustly satisfied for all q spl isin q if and only if it is satisfied at each vertex q sup i of q since the number of vertices of q explodes combinatorically with the dimension of q the computation associated with the implementation of such results is often intractable the main point of this paper is to introduce a new approach to such problems aimed at alleviation of this computational complexity problem to this end the notion of approximate feasibility is introduced and the theory which follows from this definition is vertex free

diagonal stability of matrices with cyclic structure and the secant condition an existence result on diagonal solutions of a linear matrix inequality is used to study diagonal hurwitz and schur stability and to derive the secant condition for systems with cyclic structure

performance enhancement of parameter estimators via dynamic regressor extension and mixing a new procedure to design parameter estimators with enhanced performance is proposed in the technical note for classical linear regression forms it yields a new parameter estimator whose convergence is established without the usual requirement of regressor persistency of excitation the technique is also applied to nonlinear regressions with partially monotonic parameter dependence giving rise again to estimators with enhanced performance simulation results illustrate the advantages of the proposed procedure in both scenarios

probabilistic fractals and attractors in menger spaces abstract probabilistic fractals are considered as self similar sets for contraction mappings in hyperspaces of the menger probabilistic metric spaces the completeness of hyperspaces of all closed or closed and bounded or compact nonempty subsets with respect to the probabilistic hausdorff metric is studied in some general conditions of triangular norm using the properties of hyperspaces and triangular norms of h type several existence results of attractors are obtained for a finite family and a countable family of probabilistic nonlinear contractions respectively our results are generalizations in many aspects

a passivity based approach to stability of spatially distributed systems with a cyclic interconnection structure a class of distributed systems with a cyclic interconnection structure is considered these systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns in this paper a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified for these systems global stability results hold if the ldquosecantrdquo criterion is satisfied in the linear case it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic lyapunov function which extends a recent diagonal stability result to partial differential equations for reaction diffusion equations with nondecreasing coupling nonlinearities global asymptotic stability of the origin is established all of the derived results remain true for both linear and nonlinear positive diffusion terms similar results are shown for compartmental systems

on some classes of nonlinear contractions in probabilistic metric spaces motivated by a question in j x fang 2015 6 we investigate the existence of fixed points for several classes of probabilistic contractions under fang type conditions

logistic models of structured population growth abstract a general model of structured population dynamics with logistic type nonlinearity is considered the model consists of a semilinear hyperbolic partial differential equation with a linear boundary condition and an initial value the logistic nonlinearity corresponds to increased mortality as the population increases the problem is treated as an abstract semilinear evolution equation sufficient conditions are given for the solutions to converge to an equilibrium solution applications are made to age structured populations size structured populations multispecies structured populations and cell populations

meagre functions and asymptotic behaviour of dynamical systems a measurable function x j r x x a metric space is said to be c meagre if c x is non empty and for every closed set k x with k c x 1 k has 5nite lebesgue measure this concept of meagreness is shown to provide a unifying framework which facilitates a variety of characterizations extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems by way of motivation consider the initial value problem f x x 0 rn with f rn rn locally lipschitz and denote its unique solution by x t t de5ned on its maximal interval of existence i 0 let g rn r be continuous assume that x is a bounded solution of the initial value problem in which case i 0 then g x is uniformly continuous if in addition g x l1 then we may conclude by an elementary observation frequently referred to as barb alat s lemma 5 see also 18 section 21 lemma 1 that g x t 0 as t 0 since by boundedness x t approaches as t its non empty compact invariant limit set b we also conclude that b g 1 0 it follows that x t tends as t to the largest invariant subset of g 1 0 this is a short proof of theorem 1 2 of 6 the proof in 6 is based on arguments involving properties of the dow generated by the dieerential

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

common fixed point theorems in fuzzy metric spaces using the clrg property the main aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in fuzzy metric spaces in the sense of kramosil and michalek satisfying new contractive conditions employing the common limit in the range property our results generalize and extend some recent results contained in jain et al 2012 12 to generalized contractive conditions under some control functions in the process some results about multidimensional common fixed points as coupled tripled quadrupled common fixed point results are derived from our main results

common fixed point theorems of compatible and weakly compatible maps in menger spaces abstract in this paper we prove some new common fixed point theorems for compatible and weakly compatible self maps on menger space under contractive conditions our results improve and generalize the results of singh and jain b singh s jain a fixed point theorem in menger space through weak compatibility j math anal appl 301 2005 439 448 razani and shirdaryazdi a razani m shirdaryazdi a common fixed point theorem of compatible maps in menger space chaos solitons fractals 32 2007 26 34 and others

on probabilistic ψ contractions in menger probabilistic metric spaces abstract in this paper we prove some equivalence for probabilistic contractions in menger probabilistic metric spaces by which we answer open question 3 in mihet and zaharia 2016 11 affirmatively

brief paper global nonlinear output regulation convergence based controller design in this paper we present output feedback controllers solving the global output regulation problem for a class of nonlinear systems the proposed controllers are based on the notion of convergent systems the presented solution extends well established results on the linear output regulation problem and the local nonlinear output regulation problem to the global case for lur e systems which are not necessarily in the output feedback form the proposed controllers can be found by solving the regulator equations and certain linear matrix inequalities for systems in the output feedback form with uncertain parameters and uncertain nonlinearities we provide a robust regulator that does not rely on the minimum phaseness assumption on the system which is crucial in the previous regulator designs for output feedback systems the results are illustrated by examples

a contraction theory approach to singularly perturbed systems in this technical note we revisit standard results on singular perturbations and multiple time scales using convergence analysis tools based on nonlinear contraction theory specifically assuming that the fast and slow subsystems are each partially contracting we obtain explicit bounds on the convergence rate of the trajectories to the slow manifold and on the asymptotic error between the trajectories of the singularly perturbed system and those of the reduced system as an application example we illustrate the design of a biomolecular insulation device

incremental passivity and output tracking of switched nonlinear systems this article studies incremental passivity and the output tracking problem for switched nonlinear systems the concept of incremental passivity for switched systems is given using the proposed weak storage functions furthermore conditions for a switched nonlinear system to be incrementally passive are obtained without the requirement of the incremental passivity conditions for subsystems it is shown that once the incremental passivity is assured the output tracking problem for switched systems is solvable via the designed controllers even though the problem for none of subsystems is solvable

global state synchronization in networks of cyclic feedback systems this technical note studies global asymptotic state synchronization in networks of identical systems conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory the method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling the method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system the result is illustrated for a network of biochemical oscillators

a mathematical model for the dynamics of clustering abstract the formation of several clusters arising from attracting forces between nonidentical entities or agents is a phenomenon observed in diverse fields think of people gathered through a mutual interest swarm behaviour of animals or clustering of oscillators in brain cells we introduce a dynamic model of mutually attracting agents for which we prove that the long term behaviour consists of agents organized into several groups or clusters we have completely characterized the cluster structure i e the number of clusters and their composition by means of a set of inequalities in the parameters of the model and have identified the intensity of the attraction as a key parameter governing the transition between different cluster structures the versatility of the model will be illustrated by discussing its relation to the kuramoto model and by describing how it applies to a system of interconnected water basins

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek

design of asymptotically convergent frequency estimator using contraction theory the problem of estimating unknown frequencies of a sinusoidal signal simultaneously is a classical problem in signal and system theory many approaches and algorithms are proposed in literature to develop estimators for a measurable sinusoidal signal having multiple sinusoids with unknown amplitudes frequencies and phases in this work an asymptotically convergent frequency estimator is given for estimation of n unknown frequencies of a measurable sinusoidal signal the contraction theory approach is adopted to show the asymptotic convergence of the proposed estimator in quite a simplified manner approach given here exploits the results of contraction theory related to semi contracting systems the nonlinear estimator based on dynamic system approach guarantees global boundedness and convergence of the state and frequency estimation for all initial conditions and frequency values it further ensures simultaneous globally convergent estimation of states and frequencies of a sinusoid involving multiple frequencies numerical simulations are presented for different combinations of frequencies to justify the claim

analysis of interconnected oscillators by dissipativity theory this paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension oscillators are regarded as open systems that satisfy a particular dissipation inequality it is shown that this characterization has implications for the global stability analysis of limit cycle oscillations i in isolated oscillators ii in interconnections of oscillators and iii for the global synchrony analysis in interconnections of identical oscillators

practical synchronization with diffusive couplings we investigate the problem of synchronizing nonidentical or perturbed nonlinear systems in the considered setup the systems are incapable to synchronize under diffusive couplings instead assuming the quad property for each system we derive conditions under which the synchronization error can be kept arbitrarily small by a proper choice of the interconnection structure this motivates the definition of practical synchronization as an alternative synchronization notion for nonidentical or perturbed dynamical systems the presented results are intimately related to synchronization of passive systems but it is shown that the stronger quad assumption is essential in our framework the proposed concept of practical synchronization translates directly into a notion of robust synchronization beyond that the results open the way for an investigation of synchronization phenomena on unbalanced graphs leading to the concept of cluster synchronization

common coupled fixed point results for probabilistic φ contractions in menger spaces abstract several hybrid probabilistic contractions with a gauge function are considered using the properties of the pseudo metric and the triangular norm some common coupled fixed point theorems are obtained in complete menger probabilistic metric spaces the main results are general because they do not assume any continuity or monotonicity conditions for