18,919 research outputs found

    Accessibility of Nonlinear Time-Delay Systems

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    A full characterization of accessibility is provided for nonlinear time-delay systems. It generalizes the rank condition which is known for weak controllability of linear time-delay systems, as well as the celebrated geometric approach for delay-free nonlinear systems and the characterization of their accessibility. Besides, fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time-delay systems. They are shown to impact preconceived ideas about canonical forms for nonlinear time-delay systems

    Integrability for Nonlinear Time-Delay Systems

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    In this note, the notion of integrability is defined for 1-forms defined in the time-delay context. While in the delay-free case, a set of 1-forms defines a vector space, it is shown that 1-forms computed for time-delay systems have to be viewed as elements of a module over a certain non-commutative polynomial ring. Two notions of integrability are defined, strong and weak integrability, which coincide in the delay-free case. Necessary and sufficient conditions are given to check if a set of 1-forms is strongly or weakly integrable. To show the importance of the topic, integrability of 1-forms is used to characterize the accessibility property for nonlinear time-delay systems. The possibility of transforming a system into a certain normal form is also considered

    Analysis of nonlinear time-delay systems using modules over non-commutative rings,

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    Abstract The theory of non-commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays. The left Ore ring of non-commutative polynomials deÿned over the ÿeld of meromorphic function is suggested as the framework for such a study. This approach is then generalized to a broader class of nonlinear systems with delays that are called generalized Roesser systems. Finally, the theory is applied to analyze nonlinear time-delay systems. A weak observability is deÿned and characterized, generalizing the well-known linear result. Properties of closed submodules are then developed to obtain a result on the accessibility of such systems.

    On the geometric interpretation of the Polynomial Lie Bracket for nonlinear time-delay systems

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    Time-delay systems are infinite dimensional, thus standard differential geometric tools can not be applied in a straightforward way. Though, thanks to a suitable extended Lie Bracket - or Polynomial Lie Bracket - which has been introduced recently, it is still possible to build up a geometric framework to tackle the analysis and synthesis problems for nonlinear time delay systems. The major contribution herein is to show that those geometric generalizations are not just formal, but are interpreted in terms of successive forward and backward flows similarly to the Lie Bracket of delay free vector fields

    Recurrence quantification analysis of global stock markets

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    This study investigates the presence of deterministic dependencies in international stock markets using recurrence plots and recurrence quantification analysis (RQA). The results are based on a large set of free float-adjusted market capitalization stock indices, covering a period of 15 years. The statistical tests suggest that the dynamics of stock prices in emerging markets is characterized by higher values of RQA measures when compared to their developed counterparts. The behavior of stock markets during critical financial events, such as the burst of the technology bubble, the Asian currency crisis, and the recent subprime mortgage crisis, is analyzed by performing RQA in sliding windows. It is shown that during these events stock markets exhibit a distinctive behavior that is characterized by temporary decreases in the fraction of recurrence points contained in diagonal and vertical structures.Recurrence plot, Recurrence quantification analysis, Nonlinear dynamics, International stock markets
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