Search

In this paper the invariance of the characteristic values and of the L ∞ norm of linear time-invariant (LTI) systems under lossless positive real transformations is proven. Given a LTI system with transfer function matrix G ( s ) , the transformation s ← F ( s ) with F ( s ) being an arbitrary lossless positive real function of order nF is considered, and the algebraic Riccati equations (AREs) allowing to assess some properties of the transformed system G ( F ( s ) ) are investigated. It is proven that, under such transformations, the solutions of the AREs associated to system G ( F ( s ) ) are related to those of G ( s ) . From this property, it derives that G ( F ( s ) ) and G ( s ) have the same L ∞ norm and that the characteristic values of G ( F ( s ) ) are those of G ( s ) , each with multiplicity nF.

The paper presents a generalized understanding on the dynamics of the sliding variable for discrete time sliding mode control systems via a fresh approach involving several bands in the space of the sliding variable. Using this analysis, controller parameters can be obtained once the ultimate band is chosen. It is shown that on choosing the least ultimate band, the control becomes non-switching and Gao's reaching law becomes identical to Utkin's reaching law. On other occasions, the ultimate band obtained using this approach is clearly less than that obtained in previous works using Gao's reaching law. The analysis is presented for both state feedback and multirate output feedback cases.

This study deals with the problem of set-membership identification of non-linear-in-the-parameters models. To solve this problem, this study illustrates how the Bayesian approach can be used to determine the feasible parameter set (FPS) by assuming uniform distributed estimation error and flat model prior probability distributions. The key point of the methodology is the interval evaluation of the likelihood function and the result is a set of boxes with associated credibility indices. For each box, the credibility index is in the interval (0, 1] and gives information about the amount of consistent models inside the box. The union of the boxes with credibility value equal to one provides an inner approximation of the FPS, whereas the union of all boxes provides an outer estimation. The boxes with credibility value smaller than one are located around the boundary of the FPS and their credibility index can be used to iteratively refine the inner and outer approximations up to a desired precision. The main issues and performance of the developed algorithms are discussed and illustrated by means of examples., This work has been partially grant-funded by CICYT SHERECS DPI-2011-26243 and CICYT ECOCIS (Ref.DPI2013-48243-C2-1-R) DPI-2009-13744 of the Spanish Ministry of Education and by i-Sense grant FP7-ICT-2009-6-270428 of the European Commission.