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

robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

finite time asynchronous h control for markov jump repeated scalar non linear systems with input constraints finite time control issue for a quite comprehensive class of system model that is markov jump repeated scalar nonlinear systems mjrsnss has been addressed an asynchronous controller is first proposed in mjrsnss which has less conservatism than mode dependent when the partly available mode information is encountered the input constraints associated with physical limitations in some practical applications have been fully considered which make our model more realistic this paper is concerned with the problem of finite time h control for markov jump repeated scalar nonlinear systems mjrsnss with input constraints the jumps between mjrsnss and desired mode dependent controllers are considered to be nonsynchronous the mode transition of the controllers is governed by a nonstationary markov chain which can model the different degrees of asynchronous jumps between mjrsnss and controllers with the aid of lyapunov krasovskii methodology some h performance criteria for the mjrsnss are proposed based on these criteria sufficient conditions on the existence of the desired controllers are established and then the gains of the controllers can be obtained by solving a convex optimization problem finally an example is presented to illustrate the effectiveness of our method

well posedness for nonlinear schrodinger equations with boundary forces in low dimensions by strichartz estimates abstract in this paper we study the well posedness of solutions for nonlinear schrodinger equations on one and two dimensional domains with boundary where the boundary is disturbed by an external inhomogeneous type of dirichlet or neumann force we first prove the local existence of solutions at the energy level for quadratic and superquadratic sources using the strichartz estimates on domains secondly we obtain conditional uniqueness and local stability then we prove the boundedness of solutions in the energy space to pass from the local theory to the global theory regarding subquadratic sources we appeal to classical methods and trudinger s inequality to prove the uniqueness which combined with the existence of weak energy solutions mass and energy inequalities eventually implies the continuity of solutions in time

nonlinear schrodinger equation with inhomogeneous dirichlet boundary data in this article we study the following nonlinear schrodinger equation iut u g u p 1u in a domain rn with initial condition u x 0 x and the dirichlet boundary condition u x t q x t on where q are given smooth functions the nonlinear term contributes a negative term to the energy i e g 0 we present the existence theorem for a global solution of finite energy when p 1 2 n

finite time stabilization of linear time varying continuous systems in this technical note the problem of finite time stabilization of linear time varying continuous systems is considered necessary and sufficient conditions based upon the solution to some lyapunov differential matrix equations are proposed for particular cases of interest from these conditions the design of time varying state feedback controller guaranteeing the finite time closed loop stability is presented numerical experiments illustrate the potentialities of the approach

stability robustness of interval matrices via lyapunov quadratic forms a sufficient condition for the robust stability of a class of interval matrices is derived using the lyapunov approach the matrices considered have elements which are nonlinear functions of a vector of independent and bounded parameters the robust stability condition requires that a quadratic form be positive definite in a finite number of conspicuous points of an enlarged parameter space

dilated lmi characterization for the robust finite time control of discrete time uncertain linear systems this paper provides new dilated linear matrix inequalities lmis characterizations for the finite time boundedness ftb and the finite time stability fts analysis of discrete time uncertain linear systems the dilated lmis are later used to design a robust controller for the finite time control of discrete time uncertain linear systems the relevant feature of the proposed approach is the decoupling between the lyapunov and the system matrices that allows considering a parameter dependent lyapunov function in this way the conservativeness with respect to previous results is decreased numerical examples are used to illustrate the results

finite time boundedness and l2 gain analysis for switched delay systems with norm bounded disturbance abstract finite time boundedness and finite time weighted l 2 gain for a class of switched delay systems with time varying exogenous disturbances are studied based on the average dwell time technique sufficient conditions which guarantee the switched linear system with time delay is finite time bounded and has finite time weighted l 2 gain are given these conditions are delay dependent and are given in terms of linear matrix inequalities detail proofs are given by using multiple lyapunov like functions an example is employed to verify the efficiency of the proposed method

global existence and nonexistence for nonlinear wave equations with damping and source terms we consider an initial boundary value problem for a nonlinear wave equation in one space dimension the nonlinearity features the damping term u m 1 u t and a source term of the form u p 1 u with m p 1 we show that whenever m p then local weak solutions are global on the other hand we prove that whenever p m and the initial energy is negative then local weak solutions cannot be global regardless of the size of the initial data

neumann inhomogeneous boundary value problem for the n 1 complex ginzburg landau equation abstract we study the following neumann inhomogeneous boundary value problem for the complex ginzburg landau equation on r n n 3 u t a i u b i u 2 u a b t 0 under initial condition u x 0 h x for x and neumann boundary condition u n k x t on where h k are given functions under suitable conditions we prove the existence of a global solution in h1

a nonparametrie maximum likelihood estimator for incomplete renewal data summary the problem of estimating the lifetime distribution based on data from independently and identically distributed stationary renewal processes is addressed the data are incomplete a nonparametric maximum likelihood estimate of the lifetime distribution is derived using the em algorithm the missing information principle is used to estimate the standard error of the estimated distribution the methodology is applied to a problem in the nursing profession where nurses withdraw from active service for a period of time before returning to take up post at a later date it is important that nurse manpower planners accurately predict this pattern of return the data analysed are from the northern ireland nursing profession

input output finite time stabilisation of a class of hybrid systems via static output feedback this article extends the concept of input output finite time stability io fts to a class of hybrid systems namely impulsive dynamical linear systems which are systems that exhibit jumps in the state trajectory sufficient conditions are given for the analysis of io fts and for the design of both static output and state feedback controllers guaranteeing io fts of the closed loop system in the general case the presented results require to solve feasibility problems involving either linear matrix inequalities or bilinear matrix inequalities which can be solved numerically in an efficient way by using off the shelf optimisation tools as illustrated by the proposed examples

reliable finite time sliding mode control for singular time delay system with sensor faults and randomly occurring nonlinearities abstract this paper focuses on the finite time sliding mode control problem for singular time delay system with sensor failures and uncertain nonlinearities based on the proposed sliding mode control law sufficient criteria are provided to guarantee the closed loop system is singular sliding mode finite time boundedness in both reaching phase and sliding motion phase the prescribed sliding mode control law can drive the state trajectories onto the specified sliding surface in a short time interval furthermore the singular h finite time boundedness conditions for error system have been established with sensor faults over the whole interval through the linear matrix inequalities technique gain matrices for controller and estimator can be obtained finally numerical examples have been given to demonstrate the potentials of the proposed method

admissibility analysis of stochastic singular systems with poisson switching abstract this paper addresses the mean square admissibility problem for a class of stochastic singular systems with poisson switching by using h representation approach we show the equivalence between mean square admissibility and robust admissibility of a deterministic system which is an extension of the result in the case of deterministic system 1 based on multiple lyapunov functions and matrix decomposition approaches some easily verifiable sufficient conditions without equality constraint are established and can be conveniently used to state feedback controller design some admissibility criteria are constructed for linear singular systems with poisson switching three examples including a rlc circuit and a mass spring damper system are introduced to demonstrate the validity of the theoretical results

a neumann boundary value problem for a generalized ginzburg landau equation we study the following generalized 1d ginzburg landau equation on w 0 x 0 u t 1 i m u x x a 1 ib 1 u 2u x a 2 ib 2 u 2u x 1 i n u 4u with initial and neumann boundary conditions u x 0 h x u x 0 t p t under suitable conditions we prove that there is a unique weak solution that exists for all time

finite time boundedness for switched systems with sector bounded nonlinearity and constant time delay finite time boundedness and finite time stability of switched systems with sector bounded nonlinearity and constant time delay are investigated sufficient conditions which guarantee finite time stability or finite time boundedness of the switched nonlinear system are presented respectively average dwell time of switching signals is also given moreover finite time weighted l2 gain of the switched nonlinear system is addressed to measure its disturbance tolerance capability in the fixed time interval detail proofs are accomplished by using multiple lyapunov like functions an example is employed to verify the efficiency of the proposed method

stability of stochastic nonlinear systems with state dependent switching in this paper the problem of stability on stochastic systems with state dependent switching is investigated to analyze properties of the switched system by means of ito s formula and dynkin s formula it is critical to show switching instants being stopping times when the given active region set can be replaced by its interior the local solution of the switched system is constructed by defining a series of stopping times as switching instants and the criteria on global existence and stability of solution are presented by lyapunov approach for the case where the active region set can not be replaced by its interior the switched systems do not necessarily have solutions thereby quasi solution to the underlying problem is constructed and the boundedness criterion is proposed the significance of this paper is that all the results presented depend on some easily verified assumptions that are as elegant as those in the deterministic case and the proofs themselves provide design procedures for switching controls

nonparametric estimation with recurrent event data the problem of nonparametric estimation for the distribution function governing the time to occurrence of a recurrent event in the presence of censoring is considered we derive nelson aalen and kaplan meier type estimators for the distribution function and establish their respective finite sample and asymptotic properties we allow for random observation periods for each subject under study and explicitly account for the informative sum quota nature of the data accrual scheme these allowances complicate technical matters considerably and in particular invalidate the direct use of martingale methods consistency and weak convergence of our estimators are obtained by extending an approach due to sellke who considered a single renewal process i e recurrent events on a single subject observed over an infinite time period a useful feature of the present analysis is that strong parallels are drawn to the usual single event setting providing a natural route toward developing extensions that involve

regularity theory of hyperbolic equations with non homogeneous neumann boundary conditions ii general boundary data abstract this paper studies the regularity of solutions of general mixed second order time dependent hyperbolic problems of neumann type in a previous paper i lasiecka and r triggiani ann mat pura appl iv clvii 1990 285 367 using pseudo differential calculus we have provided sharp regularity results of the solutions and their traces when the non homogeneous data are in l 2 now we complement this study by providing a regularity when the non homogeneous data are more regular than as well as less regular than l 2 in contrast with our previous paper a functional analytic approach based on the l 2 results of our previous paper is used throughout

global existence and open loop exponential stabilization of weak solutions for nonlinear schrodinger equations with localized external neumann manipulation abstract in this paper we consider the nonlinear schrodinger equations nls with focusing defocusing interior source and possibly nonlinear damping on a bounded regular domain in the euclidean space moreover it is assumed that the solutions are subject to external neumann boundary manipulation on one portion of the boundary our aim is to obtain global existence of the weak solutions under various assumptions on the sign of the source and powers of the nonlinearities in the case of a linear damping we also prove that solutions decay exponentially under the assumption that the neumann type control at the boundary decays in a similar manner

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

on finite time stability of nonautonomous nonlinear systems this paper is concerned with the finite time stability fts of nonautonomous nonlinear systems firstly a new definition of fts for nonautonomous nonlinear systems is introduced then some suffic

well posedness and energy decay estimates in the cauchy problem for the damped defocusing schrodinger equation abstract in this paper we study the existence at the h 1 level as well as the stability for the damped defocusing schrodinger equation in r d the considered damping coefficient is time dependent and may vanish at infinity to prove the existence we employ the method devised by ozsari kalantarov and lasiecka 27 which is based on monotone operators theory in particular when d 1 or d 2 we obtain the uniqueness decay estimates for the l 2 level and h 1 l p 2 level energies are established with the help of direct multipliers method coupled with refined energy estimates and a lower semi continuity argument

finite time stability and stabilization of nonlinear stochastic hybrid systems this paper deals with the problem of finite time stability and stabilization of nonlinear markovian switching stochastic systems which exist impulses at the switching instants using multiple lyapunov function theory a sufficient condition is established for finite time stability of the underlying systems furthermore based on the state partition of continuous parts of systems a feedback controller is designed such that the corresponding impulsive stochastic closed loop systems are finite time stochastically stable a numerical example is presented to illustrate the effectiveness of the proposed method

finite time stability of linear time varying systems analysis and controller design the note deals with the finite time analysis and design problems for continuous time time varying linear systems necessary and sufficient conditions and a sufficient condition for finite time stability are devised moreover sufficient conditions for the solvability of both the state and the output feedback problems are stated such results require the feasibility of optimization problems involving differential linear matrix inequalities some numerical examples illustrate the effectiveness of the proposed approach

stochastic finite time boundedness on switching dynamics markovian jump linear systems with saturated and stochastic nonlinearities in this paper problems of finite time boundedness are investigated for a class of discrete time switching dynamics markovian jump linear systems with saturated and stochastic nonlinearities the time varying transition probabilities are described by a piecewise constant matrix subject to a high level average dwell time adt switching sensor and actuator saturations are characterized by a vector valued decomposition method and the stochastic nonlinearities are approximated by a statistical method in general not all trajectories originating from the admissible initial states could be stabilized in the mean square sense or sufficient conditions are too restrictive to yield feasible solutions therefore the purpose of studying the problems addressed here is to design an output feedback controller via the adt approach such that the resulting closed loop systems are stochastically finite time bounded and have a guaranteed disturbance attenuation capability simulation results demonstrate the potential and effectiveness of the theoretical results

a remark on the blowing up of solutions to the cauchy problem for nonlinear schrodinger equations on considere des solutions de iu t u u p 1 u u o u 0 ou x appartient a un domaine lisse cr n et on demontre que sous de bonnes conditions sur p n et u 0 h 2 h 0 1 u t l 2 eclate en un temps fini

finite time annular domain stability of impulsive switched systems mode dependent parameter approach this paper investigates the finite time stability of impulsive switched systems by applying mode dependent parameter approach and average impulsive switched interval technique the conditions that

finite time stability and stabilization for ito type stochastic markovian jump systems with generally uncertain transition rates abstract this paper investigates the problems of finite time stability and stabilization for stochastic markovian jump systems with generally uncertain transition rates smjswgutrs firstly a less conservative stability criterion is presented by a mode dependent approach then the state feedback controller and observer based controller are designed by a cone complementary linearization method and two specific algorithms are presented finally an example is used to illustrate our results

sufficient conditions for finite time stability and stabilization of nonlinear quadratic systems in this paper we deal with the finite time stability problem for quadratic systems such class of systems plays an important role in the modeling of a wide class of nonlinear processes electrical robotic biological etc the main results of the paper consist of two sufficient conditions for finite time stability analysis and finite time stabilization via static state feedback both conditions are given in terms of the feasibility of a convex optimization problem involving linear matrix inequalities a numerical example illustrates the applicability of the proposed technique

finite time control of discrete time linear systems in this note we consider the finite time stabilization of discrete time linear systems subject to disturbances generated by an exosystem finite time stability can be used in all those applications where large values of the state should not be attained for instance in the presence of saturations the main result provided in the note is a sufficient condition for finite time stabilization via state feedback this result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite time stability all the conditions are then reduced to feasibility problems involving linear matrix inequalities lmis some numerical examples are presented to illustrate the proposed methodology

technical communique finite time control of linear systems subject to parametric uncertainties and disturbances in this paper we consider finite time control problems for linear systems subject to time varying parametric uncertainties and to exogenous constant disturbances the main result provided is a sufficient condition for robust finite time stabilization via state feedback it can be applied to problems with both non zero initial conditions and unknown constant disturbances this condition is then reduced to a feasibility problem involving linear matrix inequalities lmis a detailed example is presented to illustrate the proposed methodology

weakly damped focusing nonlinear schrodinger equations with dirichlet control abstract in this article we consider the weakly damped focusing nonlinear schrodinger equations on bounded domains at the natural h 1 energy level with dirichlet control acting on a portion of the boundary we introduce the dynamic extension method for homogenizing the inhomogeneous boundary input then we construct approximate solutions using monotone operator theory a hidden trace regularity is proved to control the norm of the solutions in a global sense this allows the use of compactness techniques by which we prove the existence of weak solutions finally using multiplier techniques we prove the exponential decay of solutions under the assumption that the boundary control also decays in a similar fashion

qualitative properties of solutions for nonlinear schrodinger equations with nonlinear boundary conditions on the half line in this paper we study the interaction between a nonlinear focusing robin type boundary source a nonlinear defocusing interior source and a weak damping term for nonlinear schrodinger equations posed on the infinite half line we construct solutions with negative initial energy satisfying a certain set of conditions which blow up in finite time in the h1 sense we obtain a sufficient condition relating the powers of nonlinearities present in the model which allows construction of blow up solutions in addition to the blow up property we also discuss the stabilization property and the critical exponent for this model

finite time control of interconnected impulsive switched systems with time varying delay in this paper the problem of finite time control is addressed for a class of interconnected impulsive switched systems with time varying delay and dynamical disturbance the concepts of finite time stability and finite time boundedness are extended to interconnected impulsive switched systems respectively by resorting to the average dwell time approach and constructing an appropriate lyapunov krasovskii functional some sufficient criteria are provided to cope with the problems of finite time boundedness and finite time stability then based on the decentralized switched control scheme a state feedback controller is established to ensure the finite time stability and the finite time boundedness finally an example and simulation result are demonstrated to illustrate the correctness and effectiveness of the proposed method

a unified framework for asymptotic and transient behavior of linear stochastic systems abstract this paper is concerned with a unified framework for asymptotic and transient behavior of stochastic systems in order to explain this problem explicitly a concept of mean square stability is first introduced and two stability criteria are derived by utilizing an auxiliary definition of mean square t stability the relations among mean square stability mean square t stability and finite time stochastic stability are established subsequently two new sufficient conditions for the existence of state and output feedback mean square stabilization controllers are presented in terms of matrix inequalities a numerical algorithm is given to obtain the relation between min and finally an example is given to illustrate our results

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

finite time stability and stabilization of ito stochastic systems with markovian switching mode dependent parameter approach this technical note is concerned about the finite time stability and stabilization for ito stochastic systems with markovian switching a mode dependent parameter approach is proposed to give a sufficient condition for finite time stability and its superiority to common parameter approach is analyzed moreover the finite time stabilization is studied and two new sufficient conditions for the existence of state and output feedback controllers are presented in terms of coupled matrix inequalities a n mode algorithm is given for solving the obtained matrix inequalities arising from finite time stability stabilization finally an example is employed to illustrate the effectiveness of our obtained results

local exact controllability and stabilizability of the nonlinear schrodinger equation on a bounded interval this paper studies the exact controllability and the stabilization of the cubic schrodinger equation posed on a bounded interval both internal and boundary controls are considered and the results are given first in a periodic setting and next with dirichlet resp neumann boundary conditions it is shown that the systems with either an internal control or a boundary control are locally exactly controllable in the classical sobolev space h s for any s geq0 it is also shown that the systems with an internal stabilization are locally exponentially stabilizable in h s for any s geq0

finite time stability and stabilisation with polyhedral domains for linear systems this paper deals with finite time stability boundedness and stabilisation of discrete time linear systems with regards to polyhedral domains the key observation made in this paper is that finite

robust finite time stabilisation of uncertain linear systems this article deals with the problem of finite time stability and stabilisation of uncertain linear systems for linear time varying systems subject to norm bounded uncertainties some conditions for finite time stability are provided these conditions are expressed in terms of differential linear matrix inequalities then the problem of controller design is tackled both for the state feedback and for the output feedback case in both cases the controller can be found solving a suitable set of lmis a typical engineering case study is included to illustrate the applicability of the devised conditions

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

finite time stabilization for a class of switched time delay systems under asynchronous switching switched control systems can be used to describe many practical processes with switching phenomena such as power electronics mechanical systems etc in this paper the problem of finite time stabilization under asynchronous switching is dealt with for a class of switched time delay systems with nonlinear disturbances firstly the nonlinear uncertainties are transformed into the linear time varying forms via the differential mean value theorem under some assumptions secondly by applying the average dwell time method and convexity principle a finite time stability condition for the unforced switched time delay system is established finally an asynchronous switching state feedback controller is designed which renders the considered system finite time stable a numerical example is provided to show the effectiveness of the developed results

an inhomogeneous boundary value problem for nonlinear schrodinger equations abstract we consider a nonlinear schrodinger equation in a domain r n with the inhomegeneous dirichlet boundary condition u q where q is a given smooth function the nonlinear term contributes a positive term to the energy we prove the existence of global solutions of finite energy

robust and non fragile finite time h control for uncertain markovian jump nonlinear systems this paper investigates the non fragile and robust finite time h control problem for a class of uncertain markovian jump nonlinear systems with bounded parametric uncertainties and norm bounded disturbance by employing stochastic analysis and linear matrix inequality techniques sufficient criteria of stochastic finite time boundedness and stochastic h finite time boundedness are first provided for the class of stochastic jump systems then a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite time bounded and have an h attention performance level by utilizing matrix decomposition approach furthermore the analysis and design of non fragile and robust finite time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite time boundeded with a prescribed attention index by using non fragile control technique in addition we also deal with the analysis and design of stochastic finite time stability and stochastic finite time stabilization all criterions can be characterized in terms of linear matrix inequalities finally two examples are also given to illustrate the effectiveness of obtained results

finite time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities this paper is concerned with the finite time stochastically stability ftss analysis of markovian jump memristive neural networks with partly unknown transition probabilities in the neural networks there exist a group of modes determined by markov chain and thus the markovian jump was taken into consideration and the concept of ftss is first introduced for the memristive model by introducing a markov switching lyapunov functional and stochastic analysis theory an ftss test procedure is proposed from which we can conclude that the settling time function is a stochastic variable and its expectation is finite the system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases more importantly a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point compared with the fixed point theorem that has been widely used in the existing results this method is more easy to implement besides the delay interval was divided into four subintervals which make full use of the information of the subsystems upper bounds of the time varying delays finally the effectiveness and superiority of the proposed method is demonstrated by two simulation examples

technical communique finite time stability theorem of stochastic nonlinear systems a new concept of finite time stability called stochastically finite time attractiveness is defined for a class of stochastic nonlinear systems described by the ito differential equation the settling time function is a stochastic variable and its expectation is finite a theorem and a corollary are given to verify the finite time attractiveness of stochastic systems based on lyapunov functions two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper

exact boundary controllability of the nonlinear schrodinger equation abstract this paper studies the exact boundary controllability of the semi linear schrodinger equation posed on a bounded domain r n with either the dirichlet boundary conditions or the neumann boundary conditions it is shown that if s n 2 or 0 s n 2 with 1 n 2 2 s or s 0 1 with n 2 then the systems are locally exactly controllable in the classical sobolev space h s around any smooth solution of the cubic schrodinger equation

brief paper finite time control of discrete time linear systems analysis and design conditions in this paper we deal with some finite time control problems for discrete time time varying linear systems first we provide necessary and sufficient conditions for finite time stability these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference lyapunov inequality then we address the design problem the proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite time sense all these conditions can be expressed in terms of lmis and therefore are numerically tractable as shown in the example included in the paper

finite time h control for a class of discrete time switched singular time delay systems subject to actuator saturation this paper concerns with the finite time h control problem for a class of discrete time switched singular time delay with actuator saturation not only linear matrix inequality conditions for the systems but also average dwell time of switching signal is given to guarantee regular causal and finite time boundedness for the discrete time switched singular time delay system moreover sufficient conditions are presented to ensure the h disturbance attenuation level and the design method of h controller is developed by solving linear matrix inequalities lmi optimization problem without any decompositions of system matrices and equivalent transformation furthermore the function in the proof procedure belongs to multiple lyapunov like functions whose advantage lies in their flexibility finally numerical examples are employed to verify the effectiveness of the proposed methods and to illustrate the significant improvement on the conservativeness of some reported results in the literature

monotonicity method applied to complex ginzburg landau type equations abstract global existence and smoothing effect are established for the complex ginzburg landau type equation in which the real and imaginary parts of the complex coefficient are multiplied by nonlinear terms with different powers the proof is based on monotonicity methods described by subdifferential operators the key lies in two modified inequalities

robust finite time h control for uncertain discrete jump systems with time delay abstract this paper addresses the robust finite time h control problem for a family of uncertain discrete time markovian jump systems with time delay initially the concepts of stochastic finite time boundedness and stochastic h finite time stabilization are given then a stochastic finite time h controller is designed such that the underlying closed loop discrete jump time delay system is stochastic finite time boundedness and satisfies a prescribed h performance level in some given finite time interval based on lyapunov approach sufficient criteria on the stochastic h finite time stabilization are established for the solvability of the problem which can be handled by a feasibility problem in the form of linear matrix inequalities with a fixed parameter finally simulation examples are presented to demonstrate the validity of the developed techniques

robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation in this paper the problem of robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation is studied first sufficient conditions that guarantee the systems singular stochastic finite time boundedness are derived via constructing a delay dependent lyapunov krasonskii functional and linear matrix inequalities lmi approaches then the results are extended to singular stochastic finite time h boundedness furthermore with these conditions and convex optimization arithmetic the design method of h controller and conditions that ensure the h disturbance attenuation level are obtained finally some numerical examples are presented to illustrate the validity and efficiency of the proposed methods

finite time synchronization of sampled data markovian jump complex dynamical networks with additive time varying delays based on dissipative theory abstract this paper is concerned with the problem of finite time synchronization issue of sampled data markovian jump complex dynamical networks mjcdns with additive time varying delays based on dissipative theory sufficient conditions to guarantee the finite time stability of mjcdns with additive time varying delays are presented sampled data control with stochastically varying sampling periods is considered the closed loop system is not just finite time bounded but also satisfies the dissipativity conditions further we handled a nonuniform sampled data controller by utilizing the properties of kronecker product combined with the appropriate lyapunov functionals technique a novel delay dependent finite time stability of dissipativity rule is derived in terms of linear matrix inequalities lmis to ensure that the delayed complex dynamical systems to be dissipative finally numerical examples are given to represent the applicability of the proposed approach

on global solutions to the initial boundary value problem for the damped nonlinear schrodinger equations where a 0 and q is a bounded domain in rn with smooth boundary x when a 0 undamped case the global existence of smooth solutions to the initial boundary value problem l 3 has been proved only when n 2 and f lu12 w lulp with p 2 brezis and gallouet cl with 2 i p i3 m tsutsumi 9 higher dimensional cases are very difficult pribl s and remain unproved as far as the author knows if we add a linear damping term iau a 0 then the mass ilull iztr1 and the energy ivu x t l dx j f lu x t l dx decay exponentially as t cc as is seen below which may assert the global existence of small smooth solutions even if the nonlinear term f lul u does not have a proper sign it is our purpose to establish the global existence and decay estimates of smooth solutions of the problem l 3 with small data there are a number of works on the nonlinear evolution equations see 3 5 71 and their references in the following spirit energy and decay estimates give global existence of solutions if the damping term is not added there is no hope that the decay estimates of solutions in some f q p 2 2 can be obtained since

uniform decay rates for the energy of weakly damped defocusing semilinear schrodinger equations with inhomogeneous dirichlet boundary control abstract in this paper we study the open loop stabilization as well as the existence and regularity of solutions of the weakly damped defocusing semilinear schrodinger equation with an inhomogeneous dirichlet boundary control first of all we prove the global existence of weak solutions at the h 1 energy level together with the stabilization in the same sense it is then deduced that the decay rate of the boundary data controls the decay rate of the solutions up to an exponential rate secondly we prove some regularity and stabilization results for the strong solutions in h 2 sense the proof uses the direct multiplier method combined with monotonicity and compactness techniques the result for weak solutions is strong in the sense that it is independent of the dimension of the domain the power of the nonlinearity and the smallness of the initial data however the regularity and stabilization of strong solutions are obtained only in low dimensions with small initial and boundary data

sliding mode control for markovian jump repeated scalar nonlinear systems with packet dropouts the uncertain occurrence probabilities case abstract this paper studies the sliding mode based control problem for a class of delayed markovian jump repeated scalar nonlinear systems rsnss subject to packet dropouts pds and randomly occurring uncertainties rous here the phenomenon of the markovian pds is modeled by utilizing a random variable obeying markov process by using the bernoulli distributed random variables the rous under uncertain occurrence probabilities uops are characterized from the mathematical perspective in addition the time delay considered is bounded time varying with known upper and lower bounds the attention is on designing a sliding mode based control method for markovian jump rsnss in the simultaneous presence of markovian pds rous and time varying delays specifically the robustly asymptotically mean square stability is ensured for corresponding sliding mode dynamics by proposing new sufficient criterion moreover the reachability in discrete setting is analyzed i e the state trajectories of the system from any initial condition are globally driven onto a small region nearby the pre designed sliding surface in mean square sense by synthesizing a robust sliding mode control smc law finally the effectiveness of developed control method is verified by some simulations

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective