Converse Barrier Functions via Lyapunov Functions

Weak Converse Lyapunov Theorems and Control-Lyapunov Functions

Given a weakly uniformly globally asymptotically stable closed (not necessarily compact) set A for a differential inclusion that is defined on Rn, is locally Lipschitz on Rn\A, and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on Rn. Using this result, we show that uniform global asymptotic controllability to a closed (not necessarily compact)...

Local Self-concordance of Barrier Functions Based on Kernel-functions

 Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functio...

Information Measures via Copula Functions

In applications of differential geometry to problems of parametric inference, the notion of divergence is often used to measure the separation between two parametric densities. Among them, in this paper, we will verify measures such as Kullback-Leibler information, J-divergence, Hellinger distance, -Divergence, … and so on. Properties and results related to distance between probability d...

Nondecreasing Lyapunov functions

We propose the notion of nondecreasing Lyapunov functions which can be used to prove stability or other properties of the system in question. This notion is in particular useful in studying switched or hybrid systems. We illustrate the concept by a general construction of such a nondecreasing Lyapunov function for a class of planar hybrid systems. It is noted that this class encompasses switche...

On quadratic Lyapunov functions