this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

This paper provides a Lyapunov-based small-gain theorem for input-to-state stability (ISS) of networks composed infinitely many finite-dimensional systems. We model these on infinite-dimensional ? ? -type spaces. A crucial assumption in our results is that the internal Lyapunov gains, modeling influence subsystems each other, are linear functions. Moreover, gain operator built from gains assume...

the term “system” is defined as «elements standing interaction». this implies that a change in any given element should bring about changes in other elements of the system and thus may be used to identify the boundaries of a system. a system can be a machine, a man, or a community. each of these may be part of a greater system (super system) or include several smaller systems (subsystems). syst...

In this article, we show that an infinite network of input-to-state stable (ISS) subsystems, admitting ISS Lyapunov functions, itself admits function, provided the couplings between subsystems are sufficiently weak. The strength is described in terms properties infinite-dimensional nonlinear positive operator, built from interconnection gains. If operator induces a uniformly globally asymptotic...

The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this system as an interconnection of smaller interacting subsystems, each of these subsystems having its own functionalities. In this paper, we propose a composit...

in this paper a double-shaft turbofan engine is considered to be in the design phase. therefore its environmental condition and critical source of failures has been studied and the subsystems and components has been identified. since it is in design phase, the project encounters to the lack of specified failure data. to overcome this problem, the generic data or expert judgments on the basis of...

Abstract This article provides a survey of key papers that characterise computable functions, but also some novel insights as follows. It is argued the power algorithms at least strong functions can be proved to totally in type-theoretic translations subsystems second-order Zermelo Fraenkel set theory. Moreover, it claimed typed systems lambda calculus give rise naturally functional interpretat...