Balanced realisations of all-pass systems using exact arithmetic with application to the approximation of delay systems

Numerically well-conditioned state-space realisations for all-pass systems, such as Padé approximations to exp(-s), are derived that can be computed using exact integer arithmetic. This is then applied to the a series of functions of exp(-s). It is also shown that the H-infinity norm of the transfer function from the input to the state of a balanced realisation of the Padé approximation of exp(-s) is unity. © 2012 IEEE.

Influence of Peripheral Velocity on Vane Shear Strength of an Artificial Clay

Shearing rate is among the most important factors affecting the undrained shear strength of clays. In particular, for seismic or storm-wave loading conditions, the shearing rate is much higher than that used in many common laboratory or field tests. The testing program described here evaluates the effect of peripheral velocity on the undrained strength inferred from the shear vane test. The study was conducted on a lightly cemented bentonite-kaolinite mixture manufactured in the laboratory, which possesses many characteristics similar to those of natural materials. Results show that the shear strength increases with increasing peripheral velocity, while the residual shear strength seems to be nearly independent of rotation rate.

A PDE viewpoint on basic properties of coordination algorithms with symmetries

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. ©2009 IEEE.