caratheodory approximations and stability of solutions to non lipschitz stochastic fractional differential equations of ito doob type abstract the existence and uniqueness theorem of solutions provides an effective tool for the model validation of both deterministic and stochastic equations the objective of this paper is to establish the existence and uniqueness of solutions for a class of ito doob stochastic fractional differential equations under non lipschitz condition which is weaker than lipschitz one and contains it as a special case the solution is constructed with the aid of caratheodory approximation moreover the continuous dependence of solutions on the initial value is investigated in view of the stability of solutions in the sense of mean square finally an example is given to illustrate the theory

robust h control of t s fuzzy systems with input time varying delays a delay partitioning method abstract addressed in this paper is the robust h control issue of t s fuzzy systems with input time varying delays by means of the delay partitioning method the delay interval is partitioned into multiple unequal subintervals whose lengths satisfy a geometric sequence on this basis a modified lyapunov krasovskii functional is presented to analyze asymptotic stability of the open loop system then a state feedback controller that ensures a prescribed h performance level for the closed loop system is proposed in linear matrix inequality format finally two numerical examples are given to illustrate the effectiveness and advantages of the obtained results

non fragile synchronisation control for complex networks with missing data this article investigates the problem of non fragile synchronisation control for complex networks with time varying coupling delay and missing data a stochastic variable satisfying the bernoulli random binary distribution is utilised to model the missing data based on the gronwall s inequality an exponential synchronisation condition is obtained ensuring the exponential mean square stability of the error system then a sufficient condition for designing the non fragile synchronisation controller is proposed finally a simulation example is given to show the efficiency of the proposed design methods

ito type stochastic fuzzy differential equations with delay abstract in the paper we give some foundations for the studies of stochastic fuzzy delayed differential equations we prove the existence and uniqueness of solutions to such the equations to obtain our result we assume that the coefficients of the equation satisfy the lipschitz condition together with linear growth condition we estimate the distance between approximate solution and exact solution also the stability of solution with respect to the initial history is shown an application of stochastic fuzzy delayed differential equations in the modeling of population growth is indicated

a bound on the number of integrators needed to linearize a control system this paper considers the problem of dynamic feedback linearization for nonlinear control systems for a restricted class of dynamic compensators that correspond to adding chains of integrators to the inputs we give an upper bound on the order of the compensator that needs to be considered in the case of 2 input systems we show that this bound is sharp

trajectory generation for the n trailer problem using goursat normal form develops the machinery of exterior differential forms more particularly the goursat normal form for a pfaffian system for solving nonholonomic motion planning problems i e motion planning for systems with nonintegrable velocity constraints the authors use this technique to solve the problem of steering a mobile robot with n trailers the authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the goursat canonical form two of these transformations are studied in detail the goursat normal form for exterior differential systems is dual to the so called chained form for vector fields that has been studied previously consequently the authors are able to give the state feedback law and change of coordinates to convert the n trailer system into chained form three methods for planning trajectories for chained form systems using sinusoids piecewise constants and polynomials as inputs are presented the motion planning strategy is therefore to first convert the n trailer system into goursat form use this to find the chained form coordinates plan a path for the corresponding chained form system and then transform the resulting trajectory back into the original coordinates simulations and frames of movie animations of the n trailer system for parallel parking and backing into a loading dock using this strategy are included

control of flat systems by quasi static feedback of generalized states generalized states the state representations of which depend on time derivatives of the input are naturally used in the control design for flat systems quasi static feedback of these generalized states which involves time derivatives of the closedloop input is shown to allow control of all flat systems by feedback linearization of the tracking error dynamics this is then used in a method proposed for the analysis and design by subsystems of certain flat series connections the results are illustrated on a gantry crane example

a linear algebraic framework for dynamic feedback linearization to any accessible nonlinear system we associate a so called infinitesimal brunovsky form this gives an algebraic criterion for strong accessibility as well as a generalization of kronecker controllability indices an output function which defines a right invertible system without zero dynamics is shown to exist if and only if the basis of the brunovsky form can be transformed into a system of exact differential forms this is equivalent to the system being differentially flat and hence constitutes a necessary and sufficient condition for dynamic feedback linearizability

brief paper on state representations of time varying nonlinear systems this work considers a nonlinear time varying system described by a state representation with input u and state x a given set of functions v which is not necessarily the original input u of the system is the new input candidate the main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v these conditions rely on integrability tests that are based on a derived flag as a byproduct one obtains a sufficient condition of differential flatness of nonlinear systems

remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay in this paper we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space bc 0 r d which denotes the family of bounded continuous r d value functions f defined on 0 with norm f sup q 0 f q under non lipschitz condition with lipschitz condition being considered as a special case and a weakened linear growth condition the solution is constructed by the successive approximation

synchronization for coupled neural networks with interval delay a novel augmented lyapunov krasovskii functional method this paper is concerned with the synchronization problems for an array of neural networks with hybrid coupling and interval time varying delay first a novel augmented lyapunov krasovskii functional lkf method is proposed to develop delay dependent synchronization criteria for the networks which makes use of more relaxed conditions by employing the new type of augmented matrices with kronecker product operation the proposed method can handle a multitude of kronecker product operations in the lkf and alleviates the requirements of the positive definiteness of some conditional matrices which are usually considered in the existing methods for complex networks this leads to a significant improvement in the performance of the synchronization criteria i e less conservative synchronization results can be obtained meanwhile the case of fast time varying delay can also be handled by the proposed method furthermore based on the derived criteria a robust synchronization criterion is obtained for the system with uncertainties both in coefficient and coupling matrix terms since an expression based on linear matrix inequality is used the proposed criteria can be easily checked in practice finally numerical examples are provided to show the effectiveness of the proposed method

some basic structural properties of generalized linear systems abstract this paper shows how to give a kalman state variable realization to generalized linear systems simple characterizations of controllability observability of their duality and of a minimal realization are proposed our techniques based on elementary module theory are applicable to time varying systems as well as constant systems the note ends with a brief discussion of asymptotic observers in the constant case

a constructive condition for dynamic feedback linearization the paper deals with dynamic feedback linearization of continuous time affine systems a constructive procedure based on prolongations is proposed based on necessary geometric conditions the algorithm computes a set of prolongation indices

existence uniqueness and stability of mild solutions for second order neutral stochastic evolution equations with infinite delay and poisson jumps in this paper we study a class of second order neutral stochastic evolution equations with infinite delay and poisson jumps snseeips in which the initial value belongs to the abstract space b we establish the existence and uniqueness of mild solutions for snseeips under non lipschitz condition with lipschitz condition being considered as a special case by means of the successive approximation furthermore we give the continuous dependence of solutions on the initial data by means of a corollary of the bihari inequality an application to the stochastic nonlinear wave equation with infinite delay and poisson jumps is given to illustrate the theory

exponential synchronization of lure complex dynamical networks with uncertain inner coupling and pinning impulsive control this paper is concerned with the exponential synchronization of lure type complex dynamical networks with uncertain coupling strength a novel pinning impulsive controller is designed to achieve synchronization in which only selection of nodes are chosen to control instead of the whole network in addition the proposed control scheme is digital and it can lead to low installation cost and less time in order to realize synchronization of lure type complex dynamical networks crucial delay dependent stability conditions are derived by utilizing lyapunov functional together with information of the time varying delay and convex combination technique the resulting stability conditions are formulated in the form of linear matrix inequalities lmis and by solving the obtained lmis desired impulsive control gain matrices are calculated which are capable to guarantee the exponential stability of error system finally the effectiveness of the proposed method is demonstrated through numerical simulations

robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay this paper establishes the existence and uniqueness theorem of neutral stochastic functional differential equations with infinite delay and examines the almost sure stability of this solution with general decay rate this result may be used to examine almost sure robust stability to illustrate our idea more carefully we carefully discuss a scalar stochastic integro differential equation with neutral type and its asymptotic stability including the exponential stability and the polynomial stability

the gs algorithm for exact linearization to brunovsky normal form an algorithm utilizing the minimal number of integrations for the exact linearization of nonlinear systems to brunovsky normal form under nonlinear feedback is presented the tools which are involved are based on classical constructions appearing in the theory of exterior differential systems

hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations this paper is concerned with the problem of asymptotic synchronization for a class of uncertain complex networks with delays and general uncertain perturbations in order to cope with the bad effects generated by the uncertain perturbations a novel hybrid adaptive and impulsive controller is designed such that the complex network can be asymptotically synchronized onto an isolate chaotic system with uncertain perturbations all the perturbations can be different from each other on the basis of a new lemma squeezing rule and lyapunov krasovskii functionals several sufficient conditions guaranteeing the realization of the synchronization goal are derived it is shown that the designed hybrid controllers exhibit powerful robustness some existing results are improved and extended numerical simulations verify the effectiveness of the theoretical results and the robustness of the new controller

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

global bounded synchronization of general dynamical networks with nonidentical nodes this note addresses the problem of synchronization for general dynamical networks with nonidentical nodes the coupling strength outer coupling configuration and inner connection in such networks are all time varying neither an equilibrium for each node nor a synchronization manifold is assumed to exist an estimate of the convergence domain for a general class of time varying nonlinear systems is given by introducing the average dynamics of all nodes and based on this estimate a criterion of global synchronization in the sense of boundedness of the maximum state deviation between nodes is developed an explicit bound of the maximum state deviation between nodes is obtained by the maximum difference between each node dynamics and the average dynamics the proposed criterion is an extension of several related synchronization criteria for the case of identical nodes to the case of nonidentical nodes

impulsive neutral stochastic functional integro differential equations with infinite delay driven by fbm in this paper we study a class of impulsive neutral stochastic functional integro differential equations with infinite delay driven by a standard cylindrical wiener process and an independent cylindrical fractional brownian motion fbm with hurst parameter h 1 2 1 in the hilbert space we prove the existence and uniqueness of the mild solution for this kind of equations with the coefficients satisfying some non lipschitz conditions which include the classical lipschitz conditions as special case an example is provided to illustrate the theory some well known results are generalized and extended

exact and approximate feedback linearization without the linear controllability assumption the feedback linearization problem of nonlinear control systems has been solved in the literature under the assumption that the nonlinear system is linearly controllable in this paper the assumption of linear controllability is removed necessary and sufficient conditions are given through lie orbital symmetries thus giving a geometric characterization of the problem in the analytic case both the exact and the approximate linearization problems are considered in the analytic case

a condition for dynamic feedback linearization of control affine nonlinear systems in this paper a necessary and sufficient condition for dynamic feedback linearizability by endogenous feedback of control affine nonlinear systems is presented the condition is based on a modified derived flag of a pfaffian system associated with a control system which takes into account the presence of a precompensator it is shown that the generators associated with this modified derived flag must satisfy a number of congruences the congruences ensure that the conditions of the gs algorithm are satisfied for the prolongated system and thus provide an algorithm to calculate the required feedback and state space transformations a tower structure is identified with respect to a set of indices corresponding to a set of generalized kronecker indices using these conditions a bound related to the extent of precompensation required for each input channel is obtained it is shown how linearizing outputs can be identified by studying the derived flag of the pfaffian system associated with a nonlinear system

differential flatness and absolute equivalence of nonlinear control systems this paper presents a formulation of differential flatness a concept originally introduced by fliess levine martin and rouchon in terms of absolute equivalence between exterior differential systems systems that are differentially flat have several useful properties that can be exploited to generate effective control strategies for nonlinear systems the original definition of flatness was given in the context of differential algebra and required that all mappings be meromorphic functions the formulation of flatness presented here does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems in particular it is shown that under regularity assumptions and in the case of single input control systems i e codimension 2 pfaffian systems a system is differentially flat if and only if it is feedback linearizable via static state feedback in higher codimensions our approach does not allow one to prove that feedback linearizability about an equilibrium point and flatness are equivalent one must be careful with the role of time as well as the use of prolongations that may not be realizable as dynamic feedback in a control setting applications of differential flatness to nonlinear control systems and open questions are also discussed

global synchronization of complex networks perturbed by the poisson noise in this paper the problem of stochastic synchronization analysis is investigated for complex networks perturbed by the poisson noise by using the key tool such as the infinitesimal operator for stochastic differential equations driven by the poisson process this paper proposes a globally exponentially synchronization criterion in mean square for complex networks perturbed by the poisson noise finally numerical examples are provided to demonstrate the effectiveness of the proposed approach

feedback stabilization of control systems described by a class of nonlinear differential algebraic equations a theoretical framework for the stabilization of con trol systems defined by a class of nonlinear differential alge braic equations is established assumptions are stated which guarantee that the nonlinear differential algebraic equations can be described by a nonlinear control system defined on a smooth manifold a procedure for obtaining a local state realization is developed conditions for local stabilization of a single equilibrium solution including one set of conditions which can easily be checked using standard computations are indicated

on time scaling for nonlinear systems application to linearization in this note we propose a method to analyze systems in a time scale which is varied depending on the state such as dt d tau s x where t and are the actual time scale and that of new one respectively and s x is the function which we call time scaling function analysis of the system in the new time scale enables us to investigate the intrinsic structure of the system a linearization problem in the new time scale is formulated as wide sense feedback equivalence and is solved it is also shown that the time scaling function which makes the system linear is derived as the solution of differential equations

technical communique some remarks on static feedback linearization for time varying systems this work summarizes some results about static state feedback linearization for time varying systems three different necessary and sufficient conditions are stated in this paper the first condition is the one by sluis w m 1993 a necessary condition for dynamic feedback linearization systems control letters 21 277 283 the second and the third are the generalizations of known results due respectively to aranda bricaire e moog c h pomet j b 1995 a linear algebraic framework for dynamic feedback linearization ieee transactions on automatic control 40 127 132 and to jakubczyk b respondek w 1980 on linearization of control systems bulletin del academie polonaise des sciences serie des sciences mathematiques 28 517 522 the proofs of the second and third conditions are established by showing the equivalence between these three conditions the results are re stated in the infinite dimensional geometric approach of fliess m levine j martin p rouchon p 1999 a lie backlund approach to equivalence and flatness of nonlinear systems ieee transactions on automatic control 44 5 922 937

synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude kronecker product terms the problem of synchronization is studied for complex dynamical networks with hybrid coupling delays on time scales the hybrid coupling delays consist of both discrete and distributed coupling delays some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system by employing the standard lyapunov krasovskii functional matrix expansion method to handle multitude kronecker product terms and the modified jensen s inequalities on time scale new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established interms of linear matrix inequality lmi numerical examples are included to demonstrate the effectiveness of the proposed method

exponential synchronization of linearly coupled neural networks with impulsive disturbances this brief investigates globally exponential synchronization for linearly coupled neural networks nns with time varying delay and impulsive disturbances since the impulsive effects discussed in this brief are regarded as disturbances the impulses should not happen too frequently the concept of average impulsive interval is used to formalize this phenomenon by referring to an impulsive delay differential inequality we investigate the globally exponential synchronization of linearly coupled nns with impulsive disturbances the derived sufficient condition is closely related with the time delay impulse strengths average impulsive interval and coupling structure of the systems the obtained criterion is given in terms of an algebraic inequality which is easy to be verified and hence our result is valid for large scale systems the results extend and improve upon earlier work as a numerical example a small world network composing of impulsive coupled chaotic delayed nn nodes is given to illustrate our theoretical result

on dynamic feedback linearization abstract we address the problem of transforming a nonlinear multi input system into a linear controllable one via nonsingular dynamic feedback and extended state space diffeomorphism we show that in the single input case if a system is dynamic feedback linearizable it is also static feedback linearizable we then give sufficient conditions for a class of multi input systems to be dynamic feedback linearizable all three dimensional systems with two controls and a controllable linear approximation about the origin are shown to belong to such a class

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

sufficient conditions for dynamic state feedback linearization sufficient conditions are given for the existence of a dynamic state feedback compensator for a multi input nonlinear system such that the closed loop system is transformable into a linear controllable one by an extended state space change of coordinates an example shows that the conditions are not necessary necessary conditions are also given which are shown to be sufficient when the number of states minus the number of controls is equal to one several examples illustrate how the sufficient conditions obtained lead to the design of the dynamic compensator

existence uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay in this paper we obtain the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay at phase space bc 0 r d which denotes the family of bounded continuous r d value functions f defined on 0 with norm email protected sup q 0 f q under non lipschitz condition with lipschitz condition being considered as a special case and a weakened linear growth condition the solution is constructed by the successive approximation furthermore we give the continuous dependence of solutions on the initial value by means of the corollary of bihari inequality

on state representations of nonlinear implicit systems this work considers a semi implicit system that is a pair s y where s is an explicit system described by a state representation where x t n and u t m which is subject to a set of algebraic constraints y t h t x t u t 0 where y t l an input candidate is a set of functions v v 1 v s which may depend on time t on x and on u and its derivatives up to a finite order the problem of finding a local proper state representation z g t z v with input v for the implicit system is studied in this article the main result shows necessary and sufficient conditions for the solution of this problem under mild assumptions on the class of admissible state representations of these solvability conditions rely on an integrability test that is computed from the explicit system s the approach of this article is the infinite dimensional differential geometric setting of fliess levine martin and rouchon 1999 a lie backlund approach to equivalence and flatnes

flatness based control of a single qubit gate this work considers the open loop control problem of steering a two level quantum system from any initial to any final condition the model of this system evolves on the state space having two inputs that correspond to the complex amplitude of a resonant laser field a symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations simulation results of this flatness based open loop control are provided

a necessary condition for dynamic feedback linearization abstract a necessary condition for dynamic feedback linearizability of control systems x dot f x u in which the controls enter nonlinearly is derived for each x the image of the function f x needs to allow a ruling i e a foliation by straight lines

robust global synchronization of complex networks with neutral type delayed nodes in this paper the problems of robust global exponential synchronization for a class of complex networks with time varying delayed couplings are considered each node in the network is composed of a class of delayed neural networks described by a nonlinear delay differential equation of neutral type since model errors commonly exist in practical applications the parameter uncertainties are involved in the considered model sufficient conditions that ensure the complex networks to be robustly globally exponentially synchronized are obtained by using the lyapunov functional method and some properties of kronecker product an illustrative example is presented to show the effectiveness of the proposed approach

stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks in this paper we investigate the stochastic functional differential equations with infinite delay some sufficient conditions are derived to ensure the pth moment exponential stability and pth moment global asymptotic stability of stochastic functional differential equations with infinite delay by using razumikhin method and lyapunov functions based on the obtained results we further study the pth moment exponential stability of stochastic recurrent neural networks with unbounded distributed delays the result extends and improves the earlier publications two examples are given to illustrate the applicability of the obtained results

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

second order neutral impulsive stochastic evolution equations with delay in this paper we study the second order neutral stochastic evolution equations with impulsive effect and delay snseeids we establish the existence and uniqueness of mild solutions to snseeids under non lipschitz condition with lipschitz condition being considered as a special case by the successive approximation furthermore we give the continuous dependence of solutions on the initial data by means of corollary of the bihari inequality an application to the stochastic nonlinear wave equation with impulsive effect and delay is given to illustrate the theory

asymptotically almost periodic solutions of stochastic functional differential equations abstract in this paper we investigate a class of stochastic functional differential equations of the form dx t ax t f t x t x t dt g t x t x t dw t our main results concern the existence and exponential stability of quadratic mean asymptotically almost periodic mild solutions an example is given to illustrate our results

exponential stability of the split step θ method for neutral stochastic delay differential equations with jumps abstract the exponential mean square stability of the split step method for neutral stochastic delay differential equations nsddes with jumps is considered new conditions for jumps are proposed to ensure the exponential mean square stability of the trivial solution if the drift coefficient satisfies the linear growth condition it is shown that the split step method can reproduce the exponential mean square stability of the trivial solution for the constrained stepsize then by applying the chebyshev inequality and the borel cantelli lemma the almost sure exponential stability of both the trivial solution and the numerical solution can be obtained since split step method covers euler maruyama em method and split step backward euler ssbe method the conclusions are valid for these two methods moreover they can adapt to the nsddes and the sddes with jumps finally a numerical example illustrates the effectiveness of the theoretical results

existence and stability of solutions to non lipschitz stochastic differential equations driven by levy noise in this paper successive approximation method is applied to investigate the existence and uniqueness of solutions to stochastic differential equations sdes driven by levy noise under non lipschitz condition which is a much weaker condition than lipschitz one the stability of solutions to non lipschitz sdes driven by levy noise is also considered and the stochastic stability is obtained in the sense of mean square

synchronization of a complex dynamical network with coupling time varying delays via sampled data control abstract in this paper the synchronization problem of a complex dynamical network with coupling time varying delays via delayed sampled data controller is investigated in order to make full use of the sawtooth structure characteristic of the sampling input delay a discontinuous lyapunov functional is proposed based on the extended wirtinger inequality from a convex representation of the sector restricted nonlinearity in system dynamics the stability condition based on lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time varying delay finally two numerical examples are given to illustrate the effectiveness of the proposed methods

a note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay in this note we prove the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay insfdes in short in which the initial value belongs to the phase space bc 0 r d which denotes the family of bounded continuous r d value functions f defined on 0 with norm f sup q 0 f q under some caratheodory type conditions on the coefficients by means of the successive approximation especially we extend the results appeared in ren et al y ren s lu n xia remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay j comput appl math 220 2008 364 372 ren and xia y ren n xia existence uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay appl math comput 210 2009 72 79 and zhou and xue s zhou m xue the existence and uniqueness of the solutions for neutral stochastic functional differential equations with infinite delay math appl 21 2008 75 83

exponential stability for second order neutral stochastic differential equations with impulses in this paper we investigate the problem on the exponential stability of mild solution for the second order neutral stochastic partial differential equations with impulses by utilising the cosine function theory a set of novel sufficient conditions is derived by establishing an impulsive integral inequality as a final point an example is given to illustrate the effectiveness of the obtained theory

synchronization of nonlinear singularly perturbed complex networks with uncertain inner coupling via event triggered control this study is concerned with the synchronization problem of nonlinear singularly perturbed complex networks with time varying coupling delays in an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria by developing the novel lyapunov krasovskii functional some adequate conditions which ensure the asymptotic synchronization are obtained in the form of linear matrix inequalities besides that synchronization problem of nonlinear singularly perturbed complex networks with uncertain inner coupling are also taken into account the uncertain inner coupling is represented by making use of the interval matrix approach finally simulation results are displayed to show the efficacy of the proposed theoretical results

consensus rate regulation for general linear multi agent systems under directed topology recently optimization in distributed multi agent coordination has been studied concerning convergence speed the optimal convergence speed of consensus for multi agent systems consisting of general linear node dynamics is still an open problem this paper aims to design optimal distributed consensus protocols for general identical linear continuous time cooperative systems which not only minimize some local quadric performances but also regulate the consensus rate including convergence rate and damping rate for the multi agent systems the graph topology is assumed to be fixed and directed the inverse optimal design method is utilized and the resulting optimal distributed protocols place part of close loop poles of the global disagreement systems at specified locations asymptotically while the remains far from the imaginary axis enough it turns out that for the identical linear continuous time multi agent systems the convergence speed has no upper bound the main advantages of the developed method over the lqr design method are that the resulting multi agent systems can achieve specified consensus rate asymptotically and the resulting protocols have the whole right half complex plane as its asymptotical consensus region numerical examples are given to illustrate the effectiveness of the proposed design procedures

mode dependent stochastic synchronization for markovian coupled neural networks with time varying mode delays this paper investigates the stochastic synchronization problem for markovian hybrid coupled neural networks with interval time varying mode delays and random coupling strengths the coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric a mode dependent augmented lyapunov krasovskii functional lkf is proposed where some terms involving triple or quadruple integrals are considered which makes the lkf matrices mode dependent as much as possible this gives significant improvement in the synchronization criteria i e less conservative results can be obtained in addition by applying an extended jensen s integral inequality and the properties of random variables new delay dependent synchronization criteria are derived the obtained criteria depend not only on upper and lower bounds of mode delays but also on mathematical expectations and variances of the random coupling strengths finally two numerical examples are provided to demonstrate the feasibility of the proposed results

the existence and uniqueness of the solution for stochastic functional differential equations with infinite delay abstract this paper is devoted to build the existence and uniqueness theorem of solutions to stochastic functional differential equations with infinite delay short for isfdes at phase space bc 0 r d under the uniform lipschitz condition the linear growth condition is weaked to obtain the moment estimate of the solution for isfdes furthermore the existence and uniqueness theorem of the solution for isfdes is derived and the estimate for the error between approximate solution and accurate solution is given on the other hand under the linear growth condition the uniform lipschitz condition is replaced by the local lipschitz condition the existence and uniqueness theorem is also valid for isfdes on t 0 t moreover the existence and uniqueness theorem still holds on interval t 0 where t 0 r is an arbitrary real number

rank invariants of nonlinear systems a linear algebraic framework for the analysis of rank properties of nonlinear systems is introduced this framework gives a high level interpretation of several existing algorithms built around the recursive computation of certain algebraic ranks associated with right invertibility left invertibility and dynamic decoupling furthermore it can be used to establish links between these algorithms and the differential algebraic approach as well as to solve some static and dynamic noninteracting control problems

absolute equivalence and dynamic feedback linearization abstract elie cartan s results on absolute equivalence of differential systems are shown to imply a generalization of a recent result on dynamic feedback linearization of scalar control systems

the geometry controllability and flatness property of the n bar system we propose a kinematic model of a system moving in an m 1 dimensional euclidean space and consisting of n rigid bars attached successively to each other and subject to the nonholonomic constraints that the instantaneous velocity of the source point of each bar is parallel to that bar we prove that the associated control system is controllable and feedback equivalent to the m chained form around any regular configuration as a consequence we deduce that the n bar system is flat and show that the cartesian position of the source point of the last from the top bar is a flat output the n bar system is a natural generalisation of the n trailer system and we provide a comparison of flatness properties of both systems

design of state estimator for neural networks with leakage discrete and distributed delays abstract in this paper the design problem of state estimator for neural networks with mixed time varying delays and leakage delays has been investigated by using appropriate model transformation that shifts the considered systems into the neutral type time delay systems adapting a new lyapunov krasovskii functional which takes into account the range of time delay and by making use of some inequality techniques delay dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable the criteria are formulated in terms of a set of linear matrix inequalities lmis which can be checked efficiently by use of some standard numerical packages finally three numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the presented results

a modified algorithm for invertibility in nonlinear systems the algorithm of hirschorn 1 for the construction of inverses of nonlinear systems is modified and new sufficient conditions for invertibility and inverse system for a larger class of systems are obtained for the systems which do not satisfy the invertibility conditions a characterization of input space on which the input output map is injective is derived

local exponential synchronization in complex dynamical networks with time varying delay and hybrid coupling in this paper the local exponential synchronization of complex dynamical networks with time varying delay and hybrid coupling is investigated we assume that the coupling configuration matrices are asymmetric and the inner coupling matrices are not restricted to be diagonal or positive definite through constructing the appropriate lyapunov krasovskii functional and applying the linear matrix inequality lmi technique several novel delay depend sufficient conditions and the decay rate are deduced for the local exponential synchronization moreover the derivative of the time varying delay is extended to any value finally the numerical simulations are given to show the effectiveness of the theoretical results

an algorithm for orbital feedback linearization of single input control affine systems feedback linearization is an effective design and analysis tool used in the study of nonlinear control systems however cases arise where linearizability conditions cannot be met for systems that are not linearizable by classical techniques orbital feedback linearization or feedback linearization by state dependent time scaling has been proposed to relax these conditions unfortunately approaches proposed to date have led to conditions that tend to be more difficult to check then conditions for state feedback linearization in this paper necessary and sufficient conditions for orbital feedback linearizability is presented for a class of single input nonlinear systems the conditions are simple and can be checked directly from the data of the problem using an exterior calculus approach a simple algorithm is developed to compute state dependent time scaling that yield state feedback linearizable systems it is shown that orbital feedback linearizability generalizes the concept state feedback linearizability to deal with locally weakly accessible control systems

tracking in nonlinear differential algebraic control systems with applications to constrained robot systems we consider the design of a feedback control law for control systems described by a class of nonlinear differential algebraic equations so that certain desired outputs track given reference inputs the nonlinear differential algebraic control system being considered is not in state variable form assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential algebraic equations is expressed in a familiar normal form a nonlinear feedback control law is then proposed which ensures under appropriate assumptions that the tracking error in the closed loop differential algebraic system approaches zero exponentially applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints constrained robot systems with joint flexibility and constrained robot systems with significant actuator dynamics are discussed

a note on the neutral stochastic functional differential equation with infinite delay and poisson jumps in an abstract space in this note we prove the existence and uniqueness of the solution to neutral stochastic functional differential equation with infinite delay and poisson jumps in the phase space b with non lipschitz coefficients the known results that appeared in the studies by ren and xia appl math comput 210 72 2009 ren and xiaappl math comput 214 457 2009 and xu and hu acta appl math unpublished are generalized and improved an example is provided to illustrate the theory

a lie backlund approach to equivalence and flatness of nonlinear systems a new system equivalence relation using the framework of differential geometry of jets and prolongations of infinite order is studied in this setting two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives this is a lie backlund isomorphism the authors prove that although the state dimension is not preserved the number of input channels is kept fixed they also prove that a lie backlund isomorphism can be realized by an endogenous feedback the differentially flat nonlinear systems introduced by the authors 1992 via differential algebraic techniques are generalized and the new notion of orbitally flat systems is defined they correspond to systems which are equivalent to a trivial one with time preservation or not the endogenous linearizing feedback is explicitly computed in the case of the vtol aircraft to track given reference trajectories with stability

stochastic fractional differential equations driven by levy noise under caratheodory conditions in this manuscript we initiate a study on a class of stochastic fractional differential equations driven by levy noise the existence and uniqueness theorem of solutions to equations of this class is established under global and local caratheodory conditions our analysis makes use of the caratheodory approximation as well as a stopping time technique the results obtained here generalize the main results from pedjeu and ladde chaos solitons fractals 45 279 293 2012 xu et al appl math comput 263 398 409 2015 and abouagwa et al appl math comput 329 143 153 2018 finally an application to the stochastic fractional burgers differential equations is designed to validate the theory obtained in this manuscript we initiate a study on a class of stochastic fractional differential equations driven by levy noise the existence and uniqueness theorem of solutions to equations of this class is established under global and local caratheodory conditions our analysis makes use of the caratheodory approximation as well as a stopping time technique the results obtained here generalize the main results from pedjeu and ladde chaos solitons fractals 45 279 293 2012 xu et al appl math comput 263 398 409 2015 and abouagwa et al appl math comput 329 143 153 2018 finally an application to the stochastic fractional burgers differential equations is designed to validate the theory obtained

relative flatness and flatness of implicit systems in this work we define the concept of relative flatness of a system with respect to a subsystem the subsystem associated to a set of outputs of a system is constructed and called here output subsystem it is shown that the relative flatness of a system with respect to the output subsystem implies the flatness of the corresponding implicit system obtained by setting these outputs to zero a sufficient condition of relative flatness based on a relative derived flag is presented based on these results a sufficient condition for the flatness of a class of nonlinear implicit systems is obtained