Search results for "Concave function"
showing 2 items of 2 documents
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
2016
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.
Small-gain conditions for stochastic network systems
2013
In this paper, some small-gain conditions are presented for stochastic network systems which can describe many large-scale systems with interconnections, nonlinear behaviors, uncertainties and random disturbances. One subsystem is selected as monitor with the requirement that the gains to other systems are smooth concave functions. The relations of members under the supervise of the monitor are described as bilateral plus multilateral relations of gains. For the deterministic case, the requirement on the monitor can be removed. To demonstrate the power of this result, the small-gain conditions cover interconnected system with two subsystems as a special case. Compared with the existing resu…