Interval time-varying delay is common in control process, e.g., automatic robot control system, and its stability analysis is of great significance to ensure the reliable control of industrial processes. In order to improve the conservation of the existing robust stability analysis method, this paper considers a class of linear systems with norm-bounded uncertainty and interval time-varying delay as the research object. Less conservative robust stability criterion is put forward based on augmented Lyapunov-Krasovskii functional method and reciprocally convex combination. (...) Firstly, the delay interval is partitioned into multiple equidistant subintervals, and a new Lyapunov-Krasovskii functional comprising quadruple-integral term is introduced for each subinterval. Secondly, a novel delay-dependent stability criterion in terms of linear matrix inequalities is given by less conservative Wirtinger-based integral inequality approach. Three numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion. For the first example about closed-loop control systems with interval time-varying delays, the proposed robust stability criterion could get MADB about 0.3 more than the best results in the previous literature; and, for two other uncertain systems with interval time-varying delays, the MADB results obtained by the proposed method are better than those in the previous literature by about 0.045 and 0.054, respectively. All the example results obtained in this paper clearly show that our approach is better than other existing methods. (shrink)

The nature and structure of time and time-intervals in physical, chemical and biological systems will be elucidated. The relation and dependence among time, energy and taking place of natural processes will be critically analyzed. The bio-processes taking place in nano-time intervals will be identified. Their relevance to nano-bio-science and nano-bio-technology will be developed and nano-time interval-aspect of nano-sciences and nano-technology will be advanced. -/- .

Conditional automated driving [level 3, Society of Automotive Engineers ] requires drivers to take over the vehicle when an automated system’s failure occurs or is about to leave its operational design domain. Two-stage warning systems, which warn drivers in two steps, can be a promising method to guide drivers in preparing for the takeover. However, the proper time intervals of two-stage warning systems that allow drivers with different personalities to prepare for the takeover remain unclear. This study explored the optimal (...) time intervals of two-stage warning systems with insights into the drivers’ neuroticism personality. A total of 32 drivers were distributed into two groups according to their self-ratings in neuroticism. Each driver experienced takeover under the two-stage warning systems with four time intervals. The takeover performance and subjective opinions for time intervals and situation awareness were recorded. The results showed that drivers in the 5-s time interval had the best takeover preparation. Furthermore, both the 5- and 7-s time intervals resulted in more rapid takeover reactions and were rated more appropriate and useful than the 3- and 9-s time intervals. In terms of personality, drivers with high neuroticism tended to take over immediately after receiving takeover messages, at the cost of SA deficiency. In contrast, drivers with low neuroticism responded safely by judging whether they gained enough SA. We concluded that the 5-s time interval was optimal for drivers in two-stage takeover warning systems. When considering personality, drivers with low neuroticism had no strict requirements for time intervals. However, the extended time intervals were favorable for drivers with high neuroticism in developing SA. The present findings have reference implications for designers and engineers to set the time intervals of two-stage warning systems according to the neuroticism personality of drivers. (shrink)

Most of the descriptions of interval time structures in the first order predicate calculus are based on linear time. However, in the case of intervals, abandoning the condition oflinearity (e.g.LIN in van Benthem's systems) is not sufficient. In this paper, some properties of non-linear time structures are discussed. The most important one is the characterization of location of intervals in a fork of branches. This is connected with the fact that an interval can contain non-collinear subintervals. As a (...) result of non-linearity, some basic properties of interval structures must be formulated in a weaker form. Moreover, time must be filled by intervals to indicate that time cannot pass without events occurring in it. Finally, it is shown that when intervals cannot contain non-collinear subintervals, most of the conditions described in the paper are satisfied. (shrink)

Prolepsis is a rhetorical device in which an expected future event is presented as though it was already an accomplished fact. In the speed and instantaneity of current experience, our time is structured like a prolepsis. Through an analysis of the proleptic structure of some contemporary practices, I raise questions concerning the political nature of time's interval. In the proleptic organization of time, the interval between present and future is devalued as an obstacle to an anticipated event. However, (...) with the help of Kant and Heidegger, I argue that time's interval consists of an act of temporalization which at once dissolves what has already presented itself and generates an absolutely new and singular event of time and being. The interval is an event in the process of being accomplished, and it is this properly political dimension of experience that is foreclosed in our contemporary organization of time. (shrink)

We describe how we used the interactive theorem prover Isabelle to formalise and check the laws of the Timed Interval Calculus (TIC). We also describe some important corrections to, clarifications of, and flaws in these laws, found as a result of our work.

Starting from the overwhelming view that time is metaphorically conceptualized in terms of space, this study will, on the one hand, take the time interval words into minute analysis to confirm our view of event conceptualization of time at a more basic level along with space–time metaphoric conceptualization of time at a relational level. In alignment with the epistemology of the time–space conflation of the Chinese ancestors, our view is supported by the systematic examination of evidence related to the (...) cultural origins of the conceptualization of time, through a scrutiny of the original meanings and construction of words related to intervals of time in Mandarin Chinese. This study offers a new explanation of how: the conceptualization of time in Chinese is realized through metonymic cognition and words related to specific intervals of time are coined based on the metonymic conceptualization of related events or a corresponding event schema. Five major types of event-based metonymies are identified, and their interactive functions are illustrated. Based on this evidence, we argue that the double nature of both metaphoric and metonymic time conceptualization in Mandarin Chinese lies in the fact that time interval words can be used in its time categorial sense or as a time entity which suggests the etymological origins of Chinese as ideograph. It is concluded therefore that the event-based metonymy conceptualization of time can provide better insights into the characteristics of Chinese modes of thinking and its influences on the perception of and interaction with the world. This study can also serve as good evidence for the shaping effect of language on cognition. (shrink)

This work focuses on a multiagent system with time-varying interval uncertainty in the system matrix, where multiple agents interact through an undirected topology graph and only the bounding matrices on the uncertainty in the system matrix are known. A reduced-order interval observer, which is named the reduced-order neighborhood interval observer, is designed to estimate the relative state of each agent and those of its neighbors. It is shown that the reduced-order IO can guarantee the consensus of the (...) uncertain multiagent system. Finally, simulation examples are proposed to verify the theoretical findings. (shrink)

The reversal in the relation of time and movement which Deleuze describes in his Cinema books does not only concern a change in the filmic arts. Deleuze associates it with a wider Copernican turn in science, philosophy, art and indeed modern experience as a whole. Experience no longer consists of an idea plus the time it takes to realize it. Instead, time is implicated in the determination, literally the creation of the terminus of any movement of experience. Deleuze describes this (...) open movement structure as determinable virtuality. Because it is determinable, experience as a whole is neither actual nor actualisable. The whole is virtual. I use the phrase determinable virtuality as a kind of organizational device with which to organise a study of the reversal of time and movement in Deleuze's work. I study the concept of determinability as it appears in Deleuze's reading of the relation of time and movement in Kant's description of the whole of possible experience, or the Transcendental Ideas. In a following section I take up the idea of virtuality which I trace back to Duns Scotus who uses the idea of the virtual to distinguish between univocal and equivocal movements, forms of movement which, I argue, anticipate the kinostructures and chronogeneses, or movement and time-images which Deleuze places at the center of his work on cinema. (shrink)

Cinema, like language, can be said to exist as a system of differences. In his latest book, acclaimed philosopher Jacques Rancière looks at cinematic art in comparison to its corollary forms in literature and theatre. From literature, he argues, cinema takes its narrative conventions, while at the same time effacing literature’s images and philosophy; and film rejects theatre, while also fulfilling theatre’s dream. Built on these contradictions, the cinema is the real, material space in which one is moved by the (...) spectacle of shadows. Thus, for Rancière, film is the perpetually disappointed dream of a language of images. (shrink)

In this paper I argue that warrant for Lewis’ principle of recombination presupposes warrant for a combinatorial analysis of intrinsicality, which in turn presupposes warrant for the principle of recombination. This, I claim, leads to a vicious circularity: warrant for neither doctrine can get off the ground.

Carter (Noûs 55(1):171–198, 2021) argued that while most simple positive numerical sentences are literally false, they can communicate true contents because relevance has a weakening effect on their literal contents. This paper presents a challenge for his account by considering entailments between the imprecise contents of numerical sentences and the imprecise contents of comparatives. I argue that while Carter's weakening mechanism can generate the imprecise contents of plain comparatives such as `A is taller than B', it cannot generate the imprecise (...) contents of comparatives that quantify the difference between their arguments, such as `A is exactly n times as tall as B'. I then propose an alternative theory on which intervals serve as both thick degrees on a scale and denotations of numerical expressions. I argue that the alternative theory can account for the imprecise contents of both forms of comparatives as well as the data that motivate Carter's theory. (shrink)