fixed points and stability of neutral stochastic delay differential equations in this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic mean square stability theorem with a necessary and sufficient condition is proved some well known results are improved and generalized

a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

weyl product algebras and modulation spaces we discuss algebraic properties of the weyl product acting on modulation spaces for a certain class of weight functions omega we prove that m omega p q is an algebra under the weyl product if p epsilon 1 infinity and 1 q min p p for the remaining cases p epsilon 1 infinity and min p p q infinity we show that the unweighted spaces m p m q are not algebras under the weyl product c 2007 elsevier inc all rights reserved

robust guaranteed cost control for uncertain linear differential systems of neutral type in this paper the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated the uncertainty is assumed to be norm bounded and time varying nonlinear the problem is to design a state feedback control laws such that the closed loop system is robustly stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay a criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the lyapunov method a parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities a numerical example is given to illustrate the proposed method

technical communique improved stability criterion and its applications in delayed controller design for discrete time systems this paper is concerned with the problem of delay dependent stability analysis for discrete time systems with interval like time varying delays and the problem of stabilization for discrete time linear systems via time delayed controllers the first problem is solved by applying a novel lyapunov functional and an improved delay dependent stability criterion is obtained in terms of a linear matrix inequality based on this a sufficient condition for the solvability of the second problem is presented the reduced conservatism of the proposed stability result is shown through a numerical example while the applicability of the time delayed controller design method is demonstrated by an inverted pendulum system

on the design of observer based controller of linear neutral delay differential systems in this note the observer based control problem for a class of linear delay differential systems of neutral type is investigated using the lyapunov method a criterion for asymptotic stability is derived in terms of matrix inequalities which solved by convex optimization algorithms a numerical example is given to illustrate the proposed method

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

general decentralized stabilization of large scale linear continuous and discrete time delay systems we consider the general stabilization problem of linear time invariant large scale multivariable decentralized systems with delays we have established sufficient stabilization conditions for a general class of decentralized systems namely in the continuous case the requirement is that the matrix measure of the closed loop subsystem matrices can be made sufficiently negative by appropriate local feedback control whereas in the discrete case the requirement is that the norm of the closed loop subsystem matrices can be made arbitrarily small by feedback control

stable analysis for neural networks set valued mapping method by constructing some complete metric spaces this paper investigates the stable problem for a class of neural networks on the basis of set valued mapping theory by introducing the notion of essential equilibrium point some sufficient and necessary criteria guaranteeing the existence and stability of the equilibrium point are established when the activation function and uncertain parameter vary continuously different from most of previous works on the stability problem of neural network the feature of the method used in this paper does not depend on any lyapunov functional

frequency uniform decomposition method for the generalized bo kdv and nls equations abstract sufficient and necessary conditions for the embeddings between besov spaces b p q s 1 and modulation spaces m p q s 2 are obtained moreover using the frequency uniform decomposition method we study the cauchy problem for the generalized bo kdv and nls equations for which the global well posedness of solutions with the small rough data in certain modulation spaces m 2 1 s is shown

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

positive weak solutions of semilinear second order elliptic inequalities via variational inequalities existence uniqueness and convergence of approximants of positive weak solutions for semilinear second order elliptic inequalities are obtained the nonlinearities involved in these inequalities satisfy suitable upper or lower bound conditions or monotonicity conditions the lower bound conditions are allowed to contain the critical sobolev exponents the methodology is to establish variational inequality principles for demicontinuous pseudo contractive maps in hilbert spaces by considering convergence of approximants and apply them to the corresponding variational inequalities arising from the semilinear second order elliptic inequalities examples on the existence uniqueness and convergence of approximants of positive weak solutions of the semilinear second order elliptic inequalities are given

the effect of the shape of the domain on the existence of solutions of an equation involving the critical sobolev exponent abstract we study the critical sobolev exponent equation by imposing some conditions on the shape of the domain we are able to obtain existence and multiplicity of positive solutions in particular multiplicity results for contractible domains are presented based on an approach that allows us to generalize previous work by ding who had proved an existence result for a contractible domain

sharp results for the weyl product on modulation spaces we give sufficient and necessary conditions on the lebesgue exponentsfor the weyl product to be bounded on modulation spaces the sufficient conditions are obtained as the restriction to n 2 of are

algebras of distributions suitable for phase space quantum mechanics i the twisted product of functions on r2n is extended to a algebra of tempered distributions that contains the rapidly decreasing smooth functions the distributions of compact support and all polynomials and moreover is invariant under the fourier transformation the regularity properties of the twisted product are investigated a matrix presentation of the twisted product is given with respect to an appropriate orthonormal basis which is used to construct a family of banach algebras under this product

continuity properties for modulation spaces with applications to pseudo differential calculus i we discuss continuity for weighted modulation spaces andprove that many such spaces can be obtained in a canonicalway from the corresponding standard modulation spaces we also discussthe trace operator a a 0 acting on modulationspaces the results are used to get inclusions betweenmodulation spaces and besov spaces and proving continuityfor pseudo differential operators and toeplitz operators

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

the dilation property of modulation spaces and their inclusion relation with besov spaces abstract we consider the dilation property of the modulation spaces m p q let d f t f t be the dilation operator and we consider the behavior of the operator norm d m p q m p q with respect to our result determines the best order for it and as an application we establish the optimality of the inclusion relation between the modulation spaces and besov spaces which was proved by toft j toft continuity properties for modulation spaces with applications to pseudo differential calculus i j funct anal 207 2004 399 429

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

a variational inequality theory for demicontinuous s contractive maps with applications to semilinear elliptic inequalities abstract a variational inequality theory for demicontinuous s contractive maps in hilbert spaces is established by employing the ideas of granas topological transversality such a variational inequality theory has many properties similar to those of fixed point theory for demicontinuous weakly inward s contractive maps and to those of fixed point index for condensing maps the variational inequality theory will be applied to study the existence of positive weak solutions and eigenvalue problems for semilinear second order elliptic inequalities with nonlinearities which satisfy suitable lower bound conditions involving the critical sobolev exponent there has been little discussion for such elliptic inequalities involving the critical sobolev exponent in the literature

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

stability and robust stabilization of discrete time switched systems with time delays lmi approach we present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete time linear systems subject to time delays and norm bounded uncertainties namely if these lmis are solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of switched time delay systems satisfying these conditions possesses a quadratic common lyapunov function we also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common lyapunov functions we show that even the analysis is carried out through a common lyapunov function the applied controller is mode dependent

resilient control of non linear discrete time state delay systems a class of non linear discrete time systems with state delay is considered we develop an lmi based analysis and design procedures to check primarily into the robust stability of discrete time systems with state delay and bounded non linearities then we address the robust stabilization using nominal and resilient feedback designs in both cases the trade off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism seeking computational convenience all the developed results are cast in the format of linear matrix inequalities lmis and several numerical examples are presented throughout the paper to illustrate the feasibility of the theoretical developments

stabilization analysis for discrete time systems with time delay the stabilization problem for a class of discrete time systems with time varying delay is investigated by constructing an augmented lyapunov function some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality lmi technique when norm bounded parameter uncertainties appear in the delayed discrete time system a delay dependent robust exponential stabilization criterion is also presented all of the criteria obtained in this paper are strict linear matrix inequality conditions which make the controller gain matrix can be solved directly three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results