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Robust H2/H∞-state estimation for systems with error variance constraints: the continuous-time case
Copyright [1999] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approac
An elasto-visco-plastic model for immortal foams or emulsions
A variety of complex fluids consist in soft, round objects (foams, emulsions,
assemblies of copolymer micelles or of multilamellar vesicles -- also known as
onions). Their dense packing induces a slight deviation from their prefered
circular or spherical shape. As a frustrated assembly of interacting bodies,
such a material evolves from one conformation to another through a succession
of discrete, topological events driven by finite external forces. As a result,
the material exhibits a finite yield threshold. The individual objects usually
evolve spontaneously (colloidal diffusion, object coalescence, molecular
diffusion), and the material properties under low or vanishing stress may alter
with time, a phenomenon known as aging. We neglect such effects to address the
simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully
tensorial, rheological model, equivalent to the (scalar) Bingham model.
Importantly, the model consistently describes the ability of such soft
materials to deform substantially in the elastic regime (be it compressible or
not) before they undergo (incompressible) plastic creep -- or viscous flow
under even higher stresses.Comment: 69 pages, 29 figure
Moment instabilities in multidimensional systems with noise
We present a systematic study of moment evolution in multidimensional
stochastic difference systems, focusing on characterizing systems whose
low-order moments diverge in the neighborhood of a stable fixed point. We
consider systems with a simple, dominant eigenvalue and stationary, white
noise. When the noise is small, we obtain general expressions for the
approximate asymptotic distribution and moment Lyapunov exponents. In the case
of larger noise, the second moment is calculated using a different approach,
which gives an exact result for some types of noise. We analyze the dependence
of the moments on the system's dimension, relevant system properties, the form
of the noise, and the magnitude of the noise. We determine a critical value for
noise strength, as a function of the unperturbed system's convergence rate,
above which the second moment diverges and large fluctuations are likely.
Analytical results are validated by numerical simulations. We show that our
results cannot be extended to the continuous time limit except in certain
special cases.Comment: 21 pages, 15 figure
Certain aspects of regularity in scalar field cosmological dynamics
We consider dynamics of the FRW Universe with a scalar field. Using
Maupertuis principle we find a curvature of geodesics flow and show that zones
of positive curvature exist for all considered types of scalar field potential.
Usually, phase space of systems with the positive curvature contains islands of
regular motion. We find these islands numerically for shallow scalar field
potentials. It is shown also that beyond the physical domain the islands of
regularity exist for quadratic potentials as well.Comment: 15 pages with 4 figures; typos corrected, final version to appear in
Regular and Chaotic Dynamic
Closed time path approach to the Casimir energy in real media
The closed time path formalism is applied, in the framework of open quantum
systems, to study the time evolution of the expectation value of the
energy-momentum tensor of a scalar field in the presence of real materials. We
analyze quantum fluctuations in a fully non-equilibrium scenario, when the
scalar field is interacting with the polarization degrees of freedom of matter,
described as quantum Brownian particles. A generalized analysis was done for
two types of couplings between the field and the material. On the one hand, we
considered a bilinear coupling, and on the other hand, a (more realistic)
current-type coupling as in the case of the electromagnetic field interacting
with matter. We considered the high temperature limit for the field, keeping
arbitrary temperatures for each part of the volume elements of the material. We
obtained a closed form for the Hadamard propagator, which let us study the
dynamical evolution of the expectations values of the energy-momentum tensor
components from the initial time. We showed that two contributions always take
place in the transient evolution: one of these is associated to the material
and the other one is only associated to the field. Transient features were
studied and the long-time limit was derived in several cases. We proved that in
the steady situation of a field in n + 1 dimensions, the material always
contribute unless is non-dissipative. Conversely, the proper field contribution
vanishes unless the material is non-dissipative or, moreover, at least for the
1 + 1 case, if there are regions without material. We conclude that any steady
quantization scheme in 1 + 1 dimensions must consider both contributions and we
argue why these results are physically expected from a dynamical point of view,
and also could be valid for higher dimensions based on the expected continuity
between the non-dissipative and real material cases.Comment: 28 pages, no figures. Version to appear in Phys. Rev.
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