Invariance-Like Theorems and "lim inf" Convergence Properties
نویسندگان
چکیده
Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “lim inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “lim inf” Matrosov and Smallgain theorems and are based on a “lim inf” Barbalat’s Lemma. Additional technical assumptions to have “lim” convergence are given: the “lim inf”/“lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples.
منابع مشابه
On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...
متن کاملMath 1 D , Week 2 – Cauchy Sequences , Limits Superior and Inferior , and Series
These are the lecture notes from week 2 of Ma1d, the Caltech mathematics course on sequences and series. 1. Limits Superior and Inferior So: most of the definitions and theorems we’ve developed so far for sequences are centered around the concept of convergence – we have lots of ways of talking about when things converge, where they converge to, and under what conditions they will be forced to ...
متن کاملIntegral and ideals in Riesz spaces
A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. A.M.S. SUBJECT CLASSIFICATION (2000): 28B15.
متن کاملIntergenerational equity: sup, inf, lim sup, and lim inf
We study the problem of intergenerational equity for utility streams and a countable set of agents. A numerical social welfare function is invariant to ordinal transformation, satis es a weak monotonicity condition, and an invariance with respect to concatenation of utility streams if and only if it is either the sup, inf, lim sup, or lim inf.
متن کاملLim-inf Convergence and its Compactness
We describe the Mizar formalization of the proof of compactness of lim-inf convergence given in [W33] according to [CCL]. Lim-inf convergence formalized in [W28] is a Moore-Smith convergence investigated in [Y6] and involves the concept of nets. The proof is based on the equivalence of two approaches to convergence in topological spaces: filter convergence and Moore-Smith (net) convergence. The...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Trans. Automat. Contr.
دوره 61 شماره
صفحات -
تاریخ انتشار 2016