Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

Nickel in a tropical soil treated with sewage sludge and cropped with maize in a long-term field study

Sewage sludge produced by the SABESP wastewater treatment plant (Companhia de Saneamento Básico do Estado de São Paulo), located in Barueri, SP, Brazil, may contain high contents of nickel (Ni), increasing the risk of application to agricultural soils. An experiment was carried out under field conditions in Jaboticabal, SP, Brazil, with the objective of evaluating the effects on soil properties and on maize plants of increasing rates of a sewage sludge rich in Ni that had been applied for 6 consecutive years. The experiment was located on a Typic Haplorthox soil, using an experimental design of randomized blocks with four treatments (rates of sewage sludge) and five replications. At the end of the experiment the accumulated amounts of sewage sludge applied were 0.0, 30.0, 60.0 and 67.5 t ha-1. Maize (Zea mays L.) was the test plant. Soil samples were collected 60 d after sowing at depths of 0-20 cm for Ni studies and from 0 to 10 cm and from 10 to 20 cm for urease studies. Sewage sludge did not cause toxicity or micronutrient deficiencies to maize plants and increased grain production. Soil Ni appeared to be associated with the most stable fractions of the soil organic matter and was protected against strong extracting solutions such as concentrated and hot HNO3 and HCl. Ni added to the soil by sewage sludge increased the metal concentration in the shoots, but not in the grain. The Mehlich 3 extractor was not efficient to evaluate Ni phytoavailability to maize plants. Soil urease activity was increased by sewage sludge only in the layer where the residue was applied. © 2006 Elsevier Ltd. All rights reserved.