finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information this paper studies the problem of finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information the partly usable model information is considered following a certain bernoulli distributed white noise sequence the objective of the study is to design a state feedback controller such that the augmented closed loop system is mean square stochastically finite time bounded and a tracking performance level is achieved over a finite time interval by using the mode dependent diagonally dominant lyapunov function approach some sufficient conditions are established for the existence of an admissible state feedback controller based on these a state feedback controller can be constructed by using a simple matrix decoupling approach two numerical examples and a modified general economic model are presented to demonstrate the effectiveness of our proposed approach

einstein maxwell solitons the application of the inverse scattering method to the einstein maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution

collocation solution for rlw equation with septic spline a collocation solution using the septic splines as a shape function for the regularized long wave rlw equation is presented here a linear stability analysis shows the scheme to be unconditionally stable test problems which migration and interaction of solitary waves are used to validate our scheme by calculate l 2 norm and l norm and three invariants of motion are evaluates to determine the conservation properties of the algorithm the numerical scheme is compared with other published methods and shown to be accurate and efficient

darboux transforms deep reductions and solitons explicit formalisms for deep reductions of matrix differential equations and darboux covariance properties are presented the matrix 2 2 spectral problem of the second order is considered this problem with the reduction constraints being imposed on the potentials is the first equation of the lax representation of the hirota satsuma system 1981 the two reduction cases are treated with the help of the bilinear delta forms the covariance of these forms with respect to the darboux transforms under restrictions gives rise to explicit formulas of n soliton solutions in particular the two parameter soliton solutions of the hirota satsuma system are obtained the specific feature of such solutions evolution is that the singularity appears in some parameter region the yajima oikawa system 1976 is given as an example of the technique application to a 3 3 spectral problem

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

combined breathing kink modes in the fpu lattice abstract combined breather kink modes have been observed in several systems here we show that in the fpu lattice small amplitude breathing kink modes are three soliton solutions of an associated mkdv equation since this is integrable the modes can be constructed using the backlund transform as well as finding explicit solutions we consider the stability of the combined mode using variational techniques and illustrate stability for some parameter values and instability for others

existence of exotic waves for the nonlinear dispersive mkdv equation the nonlinear dispersive mkdv equation u t u 3 x u 2 x x x 0 is proved to be painleve integrable detailed classification of its travelling waves under certain parameter conditions are obtained by the improved qualitative analysis method abundant type of solutions are shown to exist including exotic traveling waves peaked waves compacted waves looped and cusped waves very particular composite waves having two singular points

the application of bifurcation method to a higher order kdv equation abstract bifurcation method of dynamical systems is employed to investigate bifurcation of solitary waves in the higher order kdv equation u t au n u x u xxx 0 where n 1 and a r numbers of solitary waves are given for each parameter condition under some parameter conditions explicit solitary wave solutions are obtained specially some new solitary wave solutions are found for kdv or mkdv equation

discrete conservation laws and the convergence of long time simulations of the mkdv equation pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mkdv equation these solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy the standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions in this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order pseudospectral spatial discretization appear as the most robust of the numerical methods but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence

blow up of h1 solution for the nonlinear schrodinger equation we consider the blow up of the solution in h1 for the following nonlinear schrodinger equation i tu u u p 1u x rn t 0 u 0 x u0 x x rn t 0 where n 2 and 1 4 n p min n 2 n 2 5 we prove that if the initial data u0 in h1 are radially symmetric and have negative energy then the solution of in h1 blows up in finite time we do not assume that xu0 l2 and therefore our result is the generalization of the results of glassey 4 and m tsutsumi 18 for the radially symmetric case

stabilization of discrete time markovian jump linear systems via time delayed controllers this paper is concerned with the stabilization problem for a class of discrete time markovian jump linear systems with time delays both in the system state and in the mode signal the delay in the system state may be time varying the delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system we first show that the resulting closed loop system is a time varying delayed markovian jump linear system with extended state space then a sufficient condition is proposed for the design of a controller such that the closed loop system is stochastically stable finally numerical simulation is used to illustrate the developed theory

fuzzy model based quantized guaranteed cost control of nonlinear networked systems this paper is concerned with the problem of guaranteed cost control for a class of continuous time networked control systems based on the takagi sugeno fuzzy model approach in this study network induced transmission delays and packet dropouts are taken into simultaneous consideration by the improved lyapunov krasovskii functionals a less conservative delay dependent condition is proposed for the stability analysis of the resulting closed loop system furthermore the sufficient condition under which the guaranteed cost controller exists is formulated in terms of linear matrix inequalities and the suboptimum solution is obtained by a cone complementarity linearization algorithm finally numerical examples are provided to illustrate the effectiveness of the proposed method

on a kdv equation with higher order nonlinearity traveling wave solutions abstract in this work the improved tanh coth method is used to obtain wave solutions to a korteweg de vries kdv equation with higher order nonlinearity from which the standard kdv and the modified korteweg de vries mkdv equations with variable coefficients can be derived as particular cases however the model studied here include other important equations with applications in several fields of physical and nonlinear sciences periodic and soliton solutions are formally derived

exact solitary wave solutions of the generalized 2 1 dimensional boussinesq equation abstract bifurcation method of dynamical systems is employed to investigate bifurcation of solitary waves in the generalized 2 1 dimensional boussinesq equation numbers of solitary waves are given for each parameter condition under some parameter conditions exact solitary wave solutions are obtained

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere by introducing a new transformation a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system which extends fan s direct algebraic method to the case when r 4 the solutions of a first order nonlinear ordinary differential equation with a higher degree nonlinear term and fan s direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined kdv mkdv gkdv equation which is derived from a simple incompressible non hydrostatic boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere as a result by taking advantage of the new first order nonlinear ordinary differential equation with a fifth degree nonlinear term and an eighth degree nonlinear term periodic wave solutions associated with the jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing most importantly the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere which are affected by the local excitation structures in atmosphere in addition as an illustrative sample the properties of the solitary wave solution and jacobin periodic solution are shown by some figures under the consideration of heating interaction

some new nonlinear wave solutions for two 3 1 dimensional equations in this paper two methods are employed to study the nonlinear wave solutions for two 3 1 dimensional equations which can be reduced to the potential kdv equation firstly using the simplified hirota s method we present generalized multiple soliton solutions and generalized multiple singular soliton solutions in which some differentiable arbitrary functions are involved secondly by means of some special orbits of the traveling wave system and integrating approach we obtain some other nonlinear wave solutions which also include differentiable arbitrary functions our work extends pioneer s results

sharp condition of global existence for nonlinear schrodinger equation with a harmonic potential this paper discusses nonlinear schrodinger equation with a harmonic potential by constructing a different cross constrained variational problem and the so called invariant sets we derive a new threshold for blow up and global existence of solutions

the application of the auxiliary equation technique to a generalized mkdv equation with variable coefficients the auxiliary differential equation technique is employed to investigate a generalized mkdv equation with variable coefficients the jacobi elliptic function wave like solutions of the equation are expressed under several circumstances the degenerated soliton like and trigonometric function solutions are discussed in detail as the modulus of the jacobi elliptic wave like solutions tends to 1 and 0 respectively

bounded traveling waves of the burgers huxley equation abstract in order to investigate bounded traveling waves of the burgers huxley equation bifurcations of codimension 1 and 2 are discussed for its traveling wave system by reduction to center manifolds and normal forms we give conditions for the appearance of homoclinic solutions heteroclinic solutions and periodic solutions which correspondingly give conditions of existence for solitary waves kink waves and periodic waves three basic types of bounded traveling waves furthermore their evolutions are discussed to investigate the existence of other types of bounded traveling waves such as the oscillatory traveling waves corresponding to connections between an equilibrium and a periodic orbit and the oscillatory kink waves corresponding to connections of saddle focus

blow up of the critical norm for some radial l2 super critical nonlinear schrodinger equations we consider the nonlinear schr odinger equation iu t delta u u p 1 u in dimension n geq 3 in the l 2 super critical range 1 frac 4 n p frac n 2 n 2 the corresponding scaling invariant space is dot h s c with 0 s c 1 and this covers the physically relevant case n p 3 the existence of finite time blow up solutions is known let p c frac n 2 p 1 so that dot h s c subset l p c let u t in dot h s c cap dot h 1 be a radially symmetric blow up solution which blows up at 0 t infty we prove that the scaling invariant l p c norm also blows up with a lower bound u t l p c geq log t t c n p rm as t to t

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

on some classes of mkdv periodic solutions we obtain exact periodic solutions of the positive and negative modified kortweg de vries mkdv equations we examine the dynamical stability of these solitary wave lattices through direct numerical simulations while the positive mkdv breather lattice solutions are found to be unstable the two soliton lattice solution of the same equation is found to be stable similarly a negative mkdv lattice solution is found to be stable we also touch upon the implications of these results for the kdv equation

breather lattice and its stabilization for the modified korteweg de vries equation we obtain an exact solution for the breather lattice solution of the modified korteweg de vries equation numerical simulation of the breather lattice demonstrates its instability due to the breather breather interaction however such multibreather structures can be stabilized through the concurrent application of ac driving and viscous damping terms

brief paper stabilization of markovian jump linear system over networks with random communication delay this paper is concerned with the stabilization problem for a networked control system with markovian characterization we consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a markov chain the resulting closed loop system is modeled as a markovian jump linear system with two jumping parameters and a necessary and sufficient condition on the existence of stabilizing controllers is established an iterative linear matrix inequality lmi approach is employed to calculate a mode dependent solution finally a numerical example is given to illustrate the effectiveness of the proposed design method

uniqueness of ground states of some coupled nonlinear schrodinger systems and their application abstract we establish the uniqueness of ground states of some coupled nonlinear schrodinger systems in the whole space we firstly use schwartz symmetrization to obtain the existence of ground states for a more general case to prove the uniqueness of ground states we use the radial symmetry of the ground states to transform the systems into an ordinary differential system and then we use the integral forms of the system more interestingly as an application of our uniqueness results we derive a sharp vector valued gagliardo nirenberg inequality

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

new exact explicit solutions of the generalized kdv equations abstract as kdv equations are characterized by the painleve equations we show here that generalized kdv equations are characterized by euler painleve equations a plethora of exact explicit similarity solutions are found which include inverse of hypergeometric function

construction of new solutions to the fully nonlinear generalized camassa holm equations by an indirect f function method an indirect f function method is introduced to solve the generalized camassa holm equation with fully nonlinear dispersion and fully nonlinear convection c l n p taking advantage of elliptic equation this f function is used to map the solutions of the generalized camassa holm equation to those of the elliptic equation as a result we can successfully obtain in a unified way and for special values of the parameters of this equation many exact solutions expressed by various single and combined nondegenerative jacobi elliptic function solutions and their degenerative solutions soliton combined soliton solutions and triangular solutions as the modulus m is driven to 1 and 0

admissibility analysis for discrete time singular markov jump systems with asynchronous switching abstract this paper deals with admissibility analysis for discrete time singular markov jump systems smjss with asynchronous switching which means the switching of controllers is asynchronous with the switching of subsystems the switching delay and state delay are modeled as markov chains the resulting closed loop system is modeled as a singular system with a markovian jumping vector and two markovian jumping parameters a new necessary and sufficient condition for regularity causality and stability of the closed loop system is proposed based on this a state feedback controller is designed in terms of a strict linear matrix inequality lmi to guarantee the admissibility of smjss with asynchronous switching finally a numerical example is given to illustrate the effectiveness of the proposed method

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

observations on the tanh coth expansion method for finding solutions to nonlinear evolution equations abstract the tanh coth expansion method for finding solitary travelling wave solutions to nonlinear evolution equations has been used extensively in the literature it is a natural extension to the basic tanh function expansion method which was developed in the 1990s it usually delivers three types of solution namely a tanh function expansion a coth function expansion and a tanh coth expansion it is known that for every tanh function expansion solution there is a corresponding coth function expansion solution it is shown that there is a tanh coth expansion solution that is merely a disguised version of the coth solution in many papers such tanh coth solutions are erroneously claimed to be new however other tanh coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh function method similar remarks apply to tan cot and tan cot expansion solutions

performance and robustness analysis of stochastic jump linear systems using wasserstein metric this paper focuses on the performance and robustness analysis of stochastic jump linear systems in the presence of stochastic jumps state variables evolve as random process with associated time varying probability density functions consequently system analysis is performed at the density level and a proper metric is necessary to quantify the system performance in this paper wasserstein metric that measures a distance between probability density functions is employed to develop new results for the performance analysis of stochastic jump linear systems both transient and steady state performance of the systems with given initial state uncertainties can be analyzed in this framework also we prove that the convergence of the wasserstein metric implies the mean square stability we present a novel split and merge algorithm for propagation of state uncertainty in such systems overall this study provides a unifying framework for the performance and robustness analysis of general stochastic jump linear systems and not necessarily markovian that is commonly assumed the usefulness and efficiency of the proposed method are verified through numerical examples

a systematical way to find breather lattice solutions to the positive mkdv equation in this paper dependent and independent variable transformations are introduced to solve the positive mkdv equation systematically by using knowledge of elliptic equation and jacobian elliptic functions it is shown that different kinds of solutions can be obtained to the positive mkdv equation including many kinds of breather lattice solutions

darboux transformation and solutions for an equation in 2 1 dimensions painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2 1 dimensions this procedure has allowed us to obtain the lax pair darboux transformation and functions in such a way that a plethora of different solutions with solitonic behavior can be constructed iteratively

bifurcation of travelling wave solutions for the 2 1 dimensional broer kau kupershmidt equation abstract the bifurcation method of planar dynamical systems and numerical simulation method of differential equations are employed to investigate the 2 1 dimensional broer kau kupershmidt equation we obtain the sufficient conditions to guarantee the existence of the bounded travelling wave solutions including solitary wave solutions kink or anti kink wave solutions and periodic wave solutions furthermore under different parameter conditions the qualitatively different phase portraits are given and the corresponding bounded travelling waves are simulated

necessary conditions and sufficient conditions for global existence for two components nonlinear schrodinger equations in the super critical case abstract in this paper we consider two components nonlinear schrodinger equations in the super critical case we establish a necessary condition and a sufficient condition of global existence of the solution for two components nonlinear schrodinger equations these conditions are charge criterion of global existence in the super critical case thereby extending the results in the critical case furthermore we improve a blow up condition

domain wall solutions of kdv like equations with higher order nonlinearity the author considers certain nonlinear partial differential equations which are korteweg de vries kdv like equations with higher order nonlinearity it is shown that these have kink domain wall solutions for particular values of the coefficients of the nonlinear terms the solutions are compared with the standard known solution of the lambda phi 2n field theories some conservation laws for these systems of equations are also given

extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear schrodinger type equations in this paper we extended the auxiliary equation method proposed by sirendaoreji and kudryashov to construct new types of jacobi elliptic function solutions of nonlinear partial differential equations pdes in mathematical physics the effectiveness of the extended method is demonstrated by applications to three nonlinear pdes namely the 2 1 dimensional nonlinear cubic quintic ginzburg landau equation the 1 1 dimensional resonant nonlinear schrodinger s equation with dual power law nonlinearity and the generalized zakharov system of equations the solitary wave solutions or trigonometric functions solutions are obtained from the jacobi elliptic function solutions when the modulus of the jacobi elliptic functions approaches to one or zero respectively comparison between our new results and the well known results is given

the boundary forced mkdv equation an unconditionally stable numerical algorithm for the modified korteweg de vries equation based on the b spline finite element method is described the algorithm is validated through a single soliton simulation in further numerical experiments forced boundary conditions u u0 are applied at the end x 0 and the generated states of solitary waves are studied by long impulse experiments these are shown to be generated periodically with period tb proportional to u 30 and to have a limiting amplitude proportional to u0 this limit is achieved by all waves after the first provided the experiment proceeds long enough the temporal development of the derivatives u 0 t u 0 t and u 0 t is also periodic with period tb the effect of negative forcing is to generate a train of negative waves the solitary wave states generated by applying a positive impulse followed immediately by an negative impulse of equal amplitude and duration is dependent on the period of forcing the solitary waves generated by these various forcing functions possess many of the attributes of free solitons

new exact solutions for the generalized variable coefficient gardner equation with forcing term abstract in this work we study the generalized variable coefficient gardner equation gvg with nonlinear terms of any order and forcing term abundant new exact solutions for the equation are obtained by using the general mapping deformation method with the aid of symbolic computation which include several kinds of types such as jacobi elliptic wave like solutions soliton like solutions trigonometric function solutions weierstrass elliptic function solution and rational type solution some of them are found for the first time which shows that the applied method is more powerful and will be used in further works to establish more entirely new exact solutions for other kinds of nonlinear partial differential equations arising in mathematical physics

the modified kdv equation with variable coefficients exact uni bi variable travelling wave like solutions in this paper the modified korteweg de vries mkdv equation with variable coefficients vc mkdv equation is investigated via two kinds of approaches and symbolic computation on the one hand we firstly reduce the vc mkdv equation to a second order nonlinear nonhomogeneous ode using travelling wave like similarity transformation and then we obtain its many types of exact fractional solutions with one travelling wave like variable by applying some fractional transformations to the obtained nonlinear ode on the other hand we reduce the vc mkdv equation to two nonlinear pdes with variable coefficients using the anti tangent and anti hypertangent function transformations respectively and then we given its many types of exact solutions with two different travelling wave like variables by studying the obtained nonlinear pde with variable coefficients c 2008 elsevier inc all rights reserved

jamming transitions and the modified korteweg de vries equation in a two lane traffic flow abstract the two lattice models are presented to simulate the traffic flow on a two lane highway they are the lattice versions of the hydrodynamic model of traffic the one model a is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other model b is the difference equation in which both time and space variables are discrete the jamming transitions among the freely moving phase the coexisting phase and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation the modified korteweg de vries mkdv equations are derived from the lattice models near the critical point the traffic jam is described by a kink antikink solution obtained from the mkdv equation it is found that the critical point the coexisting curve and the neutral stability line decrease with increasing the rate of lane changing also the computer simulation is performed for the model b it is shown that the coexisting curves obtained from the mkdv equation are consistent with the simulation result

nonstationary l2 l filtering for markov switching repeated scalar nonlinear systems with randomly occurring nonlinearities abstract this paper is concerned with nonstationary l 2 l filtering for markov switching repeated scalar nonlinear systems msrsnss with randomly occurring nonlinearities rons where measurement output is modeled by a mode dependent random variable that satisfying bernouli distribution the new relationship are proposed to depict multiple mutually independent markov chains between original mmsrsnss and nonstationary filters by constructing a proper lyapnov function the msrsnss is stochastically stable with l 2 l performance level is guaranteed accordingly the nonstationary filters are designed where filters are characterised by a two layer structure the paper provides a numerical example verifying the efficacy of established technique

robust h_ infty fuzzy output feedback control with multiple probabilistic delays and multiple missing measurements in this paper the robust h control problem is investigated for a class of uncertain discrete time fuzzy systems with both multiple probabilistic delays and multiple missing measurements a sequence of random variables all of which are mutually independent but obey the bernoulli distribution is introduced to account for the probabilistic communication delays the measurement missing phenomenon occurs in a random way the missing probability for each sensor satisfies a certain probabilistic distribution in the interval here the attention is focused on the analysis and design of h fuzzy output feedback controllers such that the closed loop takagi sugeno t s fuzzy control system is exponentially stable in the mean square the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers which ensures the exponential stability as well as the prescribed h performance the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one that is solved by the semi definite program method simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper

linear estimation for random delay systems this paper is concerned with the linear estimation problems for discrete time systems with random delayed observations when the random delay is known online i e time stamped the random delayed system is reconstructed as an equivalent delay free one by using measurement reorganization technique and then an optimal linear filter is presented based on the kalman filtering technique however the optimal filter is time varying stochastic and does not converge to a steady state in general then an alternative suboptimal filter with deterministic gains is developed under a new criteria the estimator performance in terms of their error covariances is provided and its mean square stability is established finally a numerical example is presented to illustrate the efficiency of proposed estimators

stabilization of continuous time randomly switched systems via the lmi approach this paper is concerned on the stabilization problem of continuous time switched systems with random switching signal where the dwell time in each subsystem consists of a fixed part and random part new sufficient conditions for stabilizing controllers including mode independent case are provided in terms of lmis which could be solved directly moreover the obtained results are extended to a more general case that the corresponding operation mode of a controller experiences a disordering phenomenon without designing a controller depending on new operation modes noms a kind of controller only depending on the original operation modes ooms is proposed and satisfies a minimum variance approximation whose solvable conditions are also with lmi forms finally numerical examples are used to demonstrate the effectiveness of the proposed methods

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

stabilization of stochastic delay systems via a disordered controller abstract in this paper the stabilization for stochastic delay systems is achieved by a disordered controller different from the traditionally stabilizing controllers the controller designed here experiences a disorder between control gains and system states by exploiting the robust method the above disorder is described as a controller having special uncertainties moreover the probability distribution of such uncertainties is embodied by a bernoulli variable a sufficient condition for the existence of such a disordered controller is given with lmis where the probability is considered in its design procedure based on this description a more general but complicated case where the corresponding probability is not exact but has a uncertainty is further studied whose lmi conditions are presented too finally a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods

exact traveling wave solutions of the zakharov kuznetsov benjamin bona mahony equation abstract bifurcation method of dynamical systems is employed to investigate traveling wave solutions in the 2 1 dimensional zakharov kuznetsov benjamin bona mahony equation under some parameter conditions exact solitary wave solutions and kink wave solutions are obtained

nonlinear periodic waves solutions of the nonlinear self dual network equations the new classes of periodic solutions of nonlinear self dual network equations describing the breather and soliton lattices expressed in terms of the jacobi elliptic functions have been obtained the dependences of the frequencies on energy have been found numerical simulations of soliton lattice demonstrate their stability in the ideal lattice and the breather lattice instability in the dissipative lattice however the lifetime of such structures in the dissipative lattice can be extended through the application of ac driving terms

constructing of new exact solutions to the gkdv mkdv equation with any order nonlinear terms by g g expansion method abstract the g g expansion method is introduced to construct more general exact travelling wave solutions to the generalized kdv mkdv equation with any order nonlinear terms as a result hyperbolic function solution trigonometric function solution and rational solution with parameters are obtained when the parameters take up special values the solitary waves are also derived from the travelling wave solutions the g g expansion method presents a wider applicability for handling nonlinear wave equations

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

stability analysis of a class of hybrid stochastic retarded systems under asynchronous switching the stability of a class of hybrid stochastic retarded systems hsrss with an asynchronous switching controller is investigated in this model the controller design relies on the observed jumping parameters which are however delayed and thus can not be measured in real time precisely this delayed time interval referred to as the asynchronous switching interval is markovian and dependent on the actual switching signal the sufficient conditions under which the system is either stochastically asymptotic stable or input to state stable are obtained by applying the extended razumikhin type theorem to the asynchronous switching interval these results are less conservative as it is only required that the designed lyapunov function is non decreasing it is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying markov process which is a conclusion similar to that in asynchronous deterministic switched systems the effectiveness and correctness of the obtained results are finally verified by a numerical example

sharp condition of global existence for second order derivative nonlinear schrodinger equations in two space dimensions this paper discusses a class of second order derivative nonlinear schrodinger equations which are used to describe the upper hybrid oscillation propagation by establishing a variational problem applying the potential well argument and the concavity method we prove that there exists a sharp condition for global existence and blow up of the solutions to the nonlinear schrodinger equation in addition we also answer the question how small are the initial data the global solutions exist

robust finite time stability and stabilization of uncertain markovian jump systems with time varying delay this paper deals with the robust finite time stability and stabilization problems of uncertain stochastic delayed jump systems where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously though perturbation time varying delay and brownian motion existing at the same time two conditions checking its robust finite time stability are proposed by a mode dependent parameter approach which are different from some existing methods based on the proposed results sufficient conditions for the existence of the state feedback controller are provided with lmis which could be solved directly it is seen that all the features of the underlying system such as time varying delay perturbation diffusion mode dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite time stability finally numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods

sharp thresholds of blow up and global existence for the coupled nonlinear schrodinger system in this paper we establish two new types of invariant sets for the coupled nonlinear schrodinger system in the euclidean n space rn and derive two sharp thresholds of blow up and global existence for its solutions some analogous results for the nonlinear schrodinger system posed on the hyperbolic space hn and on the standard 2 sphere s2 are also presented our arguments and constructions are improvements of some previous works on this direction at the end we give some heuristic analysis about the strong instability of the solitary waves the relation between the two types of thresholds is a very interesting problem and we leave it as an open problem for further study

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

mode independent control of singular markovian jump systems in this paper the mode independent control problem of singular markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint a new kind of mode independent h controller satisfying a minimum variance approximation is constructed whose gain is composed of some mode dependent control gains the available probability of system mode is described by the bernoulli variable and taken into account it shows that such a probability plays an important role in system analysis and associates mode independent controller with mode dependent controllers when the probability is unknown a kind of adaptive controller is proposed such that the resulting closed loop system is robust stochastically admissible with an h performance all the proposed conditions are given in terms of linear matrix inequalities two numerical examples are used to demonstrate the effectiveness of the proposed methods

delta dressing and exact solutions for the 2 1 dimensional harry dym equation exact implicit solutions with functional parameters of the 2 1 dimensional harry dym hd equation are constructed by the delta dressing method the interrelation between the hd and modified kadomtsev petviashvili mkp equations is established within the framework of the delta dressing method knowledge of the mkp eigenfunctions allows the solutions of the 2 1 dimensional hd equation to be represented in a simple parametric form

passivity criteria for continuous time neural networks with mixed time varying delays abstract this paper is concerned with the problem of passivity analysis for uncertain continuous time neural networks with mixed time varying delays the mixed time varying delays consist of both discrete and distributed delays in which the discrete delays are assumed to be varying within a given interval in addition the uncertainties are assumed to be norm bounded by employing a novel lyapunov krasovskii functional new passivity delay interval dependent criteria are established to guarantee the passivity performance when estimating an upper bound of the derivative of the lyapunov krasovskii functional we handle the terms related to the discrete and distributed delays appropriately so as to develop less conservative results these passivity conditions are presented in terms of linear matrix inequalities which can be easily solved via standard numerical software some numerical examples are given to illustrate the effectiveness of the proposed method

bounded traveling waves of the oceanic currents motion equations the bifurcation methods of differential equations are employed to investigate traveling waves of the oceanic currents motion equations the sufficient conditions to guarantee the existence of different kinds of bounded traveling wave solutions are rigorously determined further due to the existence of a singular line in the corresponding traveling wave system the smooth periodic traveling wave solutions gradually lose their smoothness and evolve to periodic cusp waves the results of numerical simulation accord with theoretical analysis

a new method for stabilization of networked control systems with random delays we consider the stabilization problem for a class of networked control systems in the discrete time domain with random delays the sensor to controller and controller to actuator delays are modeled as two markov chains and the resulting closed loop systems are jump linear systems with two modes the necessary and sufficient conditions on the existence of stabilizing controllers are established it is shown that state feedback gains are mode dependent an iterative linear matrix inequality lmi approach is employed to calculate the state feedback gains

sliding mode control of quantized systems against bounded disturbances abstract this paper investigates the sliding mode control problem of quantized systems with simultaneous input and output disturbances in a network environment the output measurements are supposed to be quantized with a logarithmic strategy before transmitting over the digital channels the main difficulties in this design are as follows 1 there exists input output disturbances and state time delay in the plant under consideration such that model discretization is difficult to be implemented the design work is therefore forbidden to be considered in continuous time domain 2 the quantized signals piecewise constants cannot be used to synthesize a continuous time sliding mode surface 3 traditional observer technique is not effective to handle output disturbances in this paper a filtering based technique is proposed to solve these difficulties based on which a sliding mode observer based control scheme is developed to stabilize the resulting closed loop systems finally the effectiveness of the proposed methodology is illustrated via a numerical example

on stability and lq control of mjls with a markov chain with general state space we study the mean square stability and the lq control of discrete time markov jump linear systems where the markov chain has a general state space the mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a lyapunov equation and a uniformity result respectively an algorithm for testing the mean square stability is also developed based on the uniformity result the finite and infinite horizon lq problems are considered and their solutions are characterized by appropriate riccati integral equations an application to networked control systems ncs is finally presented and a simple example is studied via simulation

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

solitary wave solutions of the mkdv equation abstract a new numerical solution to the modified korteweg devries minus equation is obtained using a lumped galerkin method with quadratic b spline finite elements the motion interaction and generation of solitary waves are studied using the method new results concerning the decay of quasi soliton initial conditions are given

solitary wave solutions and kink wave solutions for a generalized kdv mkdv equation abstract bifurcation method of dynamical systems is employed to investigate solitary wave solutions and kink wave solutions of the generalized kdv mkdv equation under some parameter conditions their explicit expressions are obtained

the korteweg de vries hierarchy as dynamics of closed curves in the plane the korteweg de vries modified korteweg de vries and harry dym hierarchies of integrable systems are shown to be equivalent to a hierarchy of chiral shape dynamics of closed curves in the plane these purely local dynamics conserve an infinite number of global geometric properties of the curves such as perimeter and enclosed area several techniques used to study these integrable systems are shown to have simple differential geometric interpretations connections with incompressible inviscid fluid flow in two dimensions are suggested

integrable equations arising from motions of plane curves the motion of plane curves in klein geometry is studied it is shown that the kdv harry dym sawada kotera burgers the defocusing mkdv hierarchies the camassa holm and the kaup kupershmidt equation naturally arise from the motions of plane curves in sl 2 sim 2 sa 2 and a 2 geometries these local and nonlocal dynamics conserve global geometric quantities of curves such as perimeter and enclosed area motions of curves in euclidean special linear and similarity geometries corresponding to the traveling wave solutions of the mkdv kdv and burgers equations are discussed