The Global Solutions of Impulsive Retarded Functional Differential Equations

In this paper, we present some results on the existence of the golbal solutions of nonlinear impulsive retarded functional differential equations.

Stability and control of nonlinear systems described by retarded functional equations: a review of recent results

This paper reports on recent results in a series of the work of the authors on the stability and non-linear control for general dynamical systems described by retarded functional differential and difference equations. Both internal and external stability properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization. In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly, sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of coupled systems comprised of retarded functional differential and difference equations.

CONTROLLABILITY OF ABSTRACT RETARDED FUNCTIONAL DIFFERENTIAL SYSTEMS WITH INFINITE DELAY

This paper is concerned with the controllability of retarded functional differential systems with infinite delay in a general Banach space, via a fixed point approach. Sufficient conditions for controllability are established by using the Leray-Schauder alternative. An example is given to illustrate the results.

ASYMPTOTIC STABILITY OF RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS BY LYAPUNOV’ DIRECT METHOD

This paper is devoted to studying the asymptotic stability of retarded nonlinear functional differential equations by the method of Lyapunov functionals. Under the as-sumption that there exists a positive definite time-invariant Lyapunov functional with negative semi-definite derivative, we focus on the extra conditions to guarantee the asymptotic stability, and present a new criterion, which is less conservative than the classical one. Finally, an example is given to illustrate the effectiveness of the result.

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.

Spectrum Response Estimation for Deep-Water Floating Platforms via Retardation Function Representation

The key concept of spectrum response estimation with commercial software,such as the SESAM software tool,typically includes two main steps:finding a suitable loading spectrum and computing the response amplitude operators(RAOs) subjected to a frequency-specified wave component.In this paper,we propose a nontraditional spectrum response estimation method that uses a numerical representation of the retardation functions.Based on estimated added mass and damping matrices of the structure,we decompose and replace the convolution terms with a series of poles and corresponding residues in the Laplace domain.Then,we estimate the power density corresponding to each frequency component using the improved periodogram method.The advantage of this approach is that the frequency-dependent motion equations in the time domain can be transformed into the Laplace domain without requiring Laplace-domain expressions for the added mass and damping.To validate the proposed method,we use a numerical semi-submerged pontoon from the SESAM.The numerical results show that the responses of the proposed method match well with those obtained from the traditional method.Furthermore,the estimated spectrum also matches well,which indicates its potential application to deep-water floating structures.

A nonlinear hydroelastic method considering wave memory effect for ship load responses in irregular waves

Since the amplitude and frequency of irregular waves change with time,great difficulties are brought for solving ship load responses in random waves.To take the effect of various frequencies of irregular waves into consideration in load responses of hull,the wave memory effect is necessary.A semi-analytical method is introduced for the time-domain retardation functions,and then a nonlinear hydroelastic method considering memory effect for ships in irregular waves is proposed.Segmented self-propelling model experiments of a container ship were carried out in a towing tank,a ship motion measuring device for self-propelling model test was designed.Whipping responses of the ship in regular and irregular waves are analyzed.Finally,the calculation results are compared with those measured by segmented model experiments,and the result indicates that the memory effect has little effect on load responses of ship in regular waves,but pronounced effect on results in irregular waves.Moreover,the presented method is reasonable for the prediction of ship load responses in irregular waves.

SOME KINDS OF LIAPUNOV FUNCTIONAL IN STABILITY THEORY OF RFDE

In this paper, some kinds of Liapunov functionals are constructed. By these constructions we have obtained some criteria for the uniform asymptotic stability of zero solution of several RFDE systems. These criteria are in concise forms, easily checked and applicable.

Retard function and ship motions with forward speed in time-domain

The time-domain calculations of retard function and ship motions in waves by the direct time-domain method （DTM） and the frequency to time-domain transformation method （FTTM） are compared and analyzed. A Wigley-hull-form ship and an $60 ship moving in waves are examined, and the corresponding retard functions are in good agreement with those given by DTM and FTTM. The comparison of retard functions in different forward speeds by the two methods is observed, and the results of ship motions in forward speed are also compared with the experimental data. On this basis, the advantage and disadvantage of them are discussed.

THE POSITIVE PERIODIC SOLUTIONS OF PERIODIC RFDEs WITH INFINITE DELAY

This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.