Stability and stabilizability of linear infinite-dimensional discrete-time systems

This paper contains three results on stability and stabilizabilityof linear time invariant infinite-dimensional discrete-timesystems. (1) Power stability is characterized in transfer-functionterms using the concepts of stabilizability and detectability.(2) Under the assumption that the input operator is campact,we present a necessary and sufficient condition for stabilizabilityinvolving spectral properties of the system operator and a projectionof the infinite-dimensional system onto a certain finite-dimensionalsubspace of the state space. (3) It is shown that, if the inputand output spaces are finite-dimensional, then stabilizationby finite-dimensional dynamic output feedback is possible ifand only if the systems is detectable and stabilizable.     

Laser-induced condensation in colloid—polymer mixtures

We study a mixture of hard sphere colloidal particles and non-adsorbing polymers exposed to a plane wave external potential which represents a three-dimensional standing laser field. With computer simulations and density functional theory we investigate the structure and phase behaviour using the simple Asakura-Oosawa model. For varying laser wavelength λ we monitor the emergence of structure in response to the external field, as measured by the amplitude of the oscillations in the one-body density distribution. Between the ideal gas limit for small λ and the bulk limit of large λ there is a non-monotonic crossover that is governed by commensurability of λ and the colloid diameter. The theoretical curves are in good agreement with simulation results. Furthermore, the effect of the periodic field on the liquid-vapour transition is studied, a situation that we refer to as laser-induced condensation. Above a threshold value for λ the theoretical phase diagram indicates the stability of a ‘stacked’ fluid phase, which is a periodic succession (in the beam direction) of liquid and vapour slabs. This partially condensed phase causes a splitting of the liquid-vapour binodal leading to two critical and a triple point. All our predictions should be experimentally observable for colloid-polymer mixtures in an optical resonator.     

The Location of the Control Points in the Case of Box Splines

In this paper a theorem of Greville (1967) for univariate splinesis carried over to multivariate box splines; namely, it is shownhow the vector-valued function s(x)=x can expressed in termsof some translates of a box spline. The result means that thegraph of a spline function s(x), which is given as a linearcombination of box splines, can be viewed as a parametric splinesurface. The control points of the graph are explicitly given.     

Adaptive control of infinite-dimensional systems without parameter estimation: an overview

This paper contains an overview of adaptive control of infinite-dimensionalsystems without parameter estimation or identification. We describethe main problems and present the most comprehensive results.High-gain, low-gain and switching controllers are considered.The literature is discussed and a number of open problems areposed.     

Transfer-Function Conditions for the Stability of Neutral and Volterra Integrodifferential Systems

In this paper we study the feedback interconnection (a) of twoneutral systems and (b) of two Volterra integrodifferentialsystems. We show that under very mild assumptions the closed-loopsystem pair is internally stable iff every transfer funtionwhich occurs around the loop is holomorphic in a right halfplane containing {s: Re s0}.     

Hard discs in circular cavities: density functional theory versus simulation

Three different density functional approaches, namely the Rickayzen, Takamiya-Nakanishi and Rosenfeld approximations, have been employed to study the equilibrium particle density distributions of hard-disc fluids in hard circular cavities. Also, Monte Carlo simulations have been performed to test the theoretical results. The comparison with the simulation data shows that the Rosenfeld approximation, which is based on the fundamental geometrical measures of the particles, is better than the Takamiya-Nakanishi and Rickayzen approximations and yields good agreement with the computer simulation data even for higher densities.