Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Credit risk measures: a case of renewable energy companies

The Basel III will have a significant impact on the European banking sector. In September 2010, supervisors of various countries adopted the new rules proposed by the prudential Committee on Banking Supervision to be applied to the business of credit institutions (hereinafter called ICs) in a phased manner from 2013, assuming to its full implementation by 2019. The purpose of this new regulation is to limit the excessive risk that these institutions took on the period preceding the global financial crisis of 2008. This new regulation is known in slang by Basel III. Depending on the requirement of Basel II for banks and their supervisors to assess the soundness and adequacy of internal risk measurement and credit management systems, the development of methodologies for the validation of internal and external evaluation systems is clearly an important issue . More specifically, there is a need to develop tools to validate the systems used to generate the parameters (such as PD, LGD, EAD and ratings of perceived risk) that serve as starting points for the IRB approach for credit risk. In this context, the work is composed of a number of approaches and tools used to evaluate the robustness of these elements IRB systems.