Let d ≥ 1 be an integer and r = (r1, . . . , rd) ∈ R . We define the shift radix system τr : Z → Z by τr(a) = (a2, . . . , ad,−⌊ra⌋) (a = (a1, . . . , ad)). The shift radix system τr has the finiteness property if each a ∈ Z is eventually mapped to 0 under iterations of τr. The mapping τr can be written as τr(a) = R(r)a + v(a) where R(r) is a d × d matrix and v is a correction term. It has been...

In this note we study contractivity of monotone systems and exponential convergence positive using non-Euclidean norms. We first introduce the notion conic matrix measure as a framework to stability systems. properties measures investigate their connection with weak pairings standard measures. Using pairings, characterize incremental respect Moreover, use provide sufficient conditions for equil...

We provide new sufficient conditions for a generalized exponential input-to-state stability condition to hold. Our proofs use innovative trajectory based contractivity and cooperative systems arguments. Another key ingredient is variant of Halanay's inequality, which differs from prior Halanay inequalities because its sampling. allow arbitrarily long intervals between some consecutive sampling ...

The paper deals with a risk averse dynamic programming problem infinite horizon. First, the required assumptions are formulated to have well defined. Then Bellman equation is derived, which may be also seen as standalone reinforcement learning problem. fact that operator contraction proved, guaranteeing convergence of various solution algorithms used for problems, we demonstrate on value iterat...

Abstract The aim of this paper is the analysis exponential mean-square stability properties nonlinear stochastic linear multistep methods. In particular it known that, under certain hypothesis on drift and diffusion terms equation, contractivity visible: qualitative feature exact problem here analysed numerical perspective, to understand whether a method can provide an analogous behaviour which...