parameterization of input shapers with delays of various distribution the paper introduces a new concept for composing the input shapers by combining lumped and distributed delays particularly an analytical method is proposed to parametrize zero vibration shapers with delays of various distribution involving these delays in the shaper structure the accommodation part of the shaped response can be smoothened in a predefined manner retarded spectral properties can be achieved and the response length can be optionally adjusted within the given range next following the analytical developments a numerical algorithm based on the constrained linear least squares optimization is proposed for direct design of robust distributed delay shapers

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

uniform boundedness and stability criteria in terms of two measures for impulsive integro differential equations1research supported by nserc canada 1 this paper establishes several criteria on uniform boundedness and stability in terms of two measures for impulsive integro differential equations by the method of lyapunov functions the interplay of two different measures and the discontinuities of solutions create additional difficulties in choosing suitable minimal set of functions along which the derivative of the lyapunov function is estimated consequently very complicated analysis is required in the proof of the theorems

the behavior of solutions of linear integro differential equations with unbounded delay abstract a basic theorem on the behavior of solutions of scalar linear integro differential equations with unbounded delay is established as a consequence of this theorem a stability criterion is obtained

a new approach to stability of impulsive functional differential equations in this work a new approach to stability theory of impulsive functional differential equations is proposed instead of putting all components of the state variable x in one liapunov function several functions of partial components of x which can be much easier constructed are used so that the conditions ensuring that stability are simpler and less restrictive also an example is given to illustrate the advantages of the obtained results

global exponential stability of impulsive integro differential equation abstract in this paper an impulsive integro differential equation is considered by establishing an integro differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive integro differential equation are obtained the results extend and improve the earlier publications an example is given to demonstrate the effectiveness of the theory

periodic averaging theorems for various types of equations abstract we prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem we also present a periodic averaging theorem for a large class of retarded equations

measure functional differential equations and functional dynamic equations on time scales abstract we study measure functional differential equations and clarify their relation to generalized ordinary differential equations we show that functional dynamic equations on time scales represent a special case of measure functional differential equations for both types of equations we obtain results on the existence and uniqueness of solutions continuous dependence and periodic averaging

existence and stability of almost periodic solutions for quasilinear delay systems and the halanay inequality abstract we present some easily verifiable conditions for the existence and global asymptotical stability of almost periodic solutions to systems of delay differential equations in the form u t au t wg t ut f t where a w l r n and f t g t are almost periodic in t uniformly on from bounded subsets of c h 0 r n with this purpose we use the exponential dichotomy theory together with usual positivity arguments in particular the semigroup version of the so called perron frobenius theorem is applied to study the generalized halanay inequality finally systems with maxima are studied in detail

inverse feedback shapers for coupled multibody systems the concept of inverse feedback shapers is fully developed in this report for the case of multibody systems with strongly coupled dynamics the presented results constitute a nontrivial extension of the previous papers by the authors on input shaping focusing on effectively decoupled controlled and flexible parts as the main technical result the target mode for the inverse shaper design is identified based on an input output transformation of the multibody system into the controlled subsystem the attached residual oscillatory dynamics and an internal feedback loop representing the dynamical coupling a state feedback controller applied for the selected generalized coordinate is considered throughout this paper

exponential stability of nonlinear impulsive neutral differential equations with delays abstract in this article a nonlinear impulsive neutral differential equation with time varying delays is considered by establishing a singular impulsive delay differential inequality and transforming the n dimensional impulsive neutral delay differential equation to a 2 n dimensional singular impulsive delay differential equation some sufficient conditions ensuring the global exponential stability in pc 1 of the zero solution of an impulsive neutral differential equation are obtained the results extend and improve on earlier publications an example is given to illustrate the theory

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

stability results for impulsive functional differential equations with infinite delays abstract this paper studies the stability problems for a class of impulsive functional differential equations with infinite delays of the form x t f t x t t x t k j k x t k k 1 2 by using the liapunov functions and razumikhin technique some new razumikhin type theorems on stability are obtained

mapping based algorithm for large scale computation of quasi polynomial zeros a method for computing all zeros of a retarded quasi polynomial that are located in a large region of the complex plane is presented the method is based on mapping the quasi polynomial and on utilizing asymptotic properties of the chains of zeros first the asymptotic exponentials of the chains are determined based on the distribution diagram of the quasi polynomial secondly large regions free of zeros are defined finally the zeros are located as the intersection points of the zero level curves of the real and imaginary parts of the quasi polynomial which are evaluated over the areas of the region outside those free of zeros

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

stability analysis for a class of functional differential equations and applications abstract the problem of lyapunov stability for functional differential equations in hilbert spaces is studied the system to be considered is non autonomous and the delay is time varying known results on this problem are based on the gronwall inequality yielding relative conservative bounds on nonlinear perturbations in this paper using more general lyapunov krasovskii functional neither model variable transformation nor bounding restriction on nonlinear perturbations is required to obtain improved conditions for the global exponential stability of the system the conditions given in terms of the solution of standard riccati differential equations allow to compute simultaneously the two bounds that characterize the stability rate of the solution the proposed method can be easily applied to some control problems of nonlinear non autonomous control time delay systems

existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay abstract in this paper we discuss local and global existence and uniqueness results for first order impulsive functional differential equations with multiple delay we shall rely on a nonlinear alternative of leray schauder for the global existence and uniqueness we apply a recent nonlinear alternative of leray schauder type in frechet spaces due to m frigon and a granas resultats de type leray schauder pour des contractions sur des espaces de frechet ann sci math quebec 22 2 1998 161 168 the goal of this paper is to extend the problems considered by a ouahab local and global existence and uniqueness results for impulsive differential equations with multiple delay j math anal appl 323 2006 456 472

asymptotic behavior of solutions of impulsive delay differential equations abstract effective sufficient conditions for the asymptotic stability of the trivial solution of impulsive delay differential equation formula are obtained by investigating respectively the asymptotic behavior of the nonoscillatory solutions and oscillatory solutions of the equation

exponential stability of nonlinear impulsive neutral integro differential equations abstract in this paper a nonlinear impulsive neutral integro differential equation with time varying delays is considered by establishing a singular impulsive delay integro differential inequality and transforming the n dimensional impulsive neutral integro differential equation to a 2 n dimensional singular impulsive delay integro differential equation some sufficient conditions ensuring the global exponential stability in p c 1 of the zero solution of an impulsive neutral integro differential equation are obtained the results extend and improve the earlier publications an example is also discussed to illustrate the efficiency of the obtained results