A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the system recovers from this catastrophic situation without external intervention in finite time. Unidirectional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. The focus of this work is on the c...

The idea of self-stabilization was introduced by Edsger W. Dijkstra in 1974 [1]. Self-stabilizing algorithms enable systems to be started in an arbitrary state and still converge to a desired behavior. In this letter, we discuss the time complexity of the self-stabilizing algorithm proposed by Hsu and Huang in [2], which finds a maximal matching in a network. This algorithm is the first self-st...

A local stabilizer protocol that takes any on-line or oo-line distributed algorithm and converts it into a synchronous self-stabilizing algorithm with local monitoring and repairing properties is presented. Whenever the self-stabilizing version enters an inconsistent state, the inconsistency is detected, in O(1) time, and the system state is repaired in a local manner. The expected computation ...

In the population protocol model Angluin et al. proposed in 2004, there exists no self-stabilizing leader election protocol for complete graphs, arbitrary graphs, trees, lines, degree-bounded graphs and so on unless the protocol knows the exact number of nodes. To circumvent the impossibility, we introduced the concept of loose-stabilization in 2009, which relaxes the closure requirement of sel...

In a graph or network G = (V;E), a set S V is k-dependent if no node in S has more than k neighbors in S. We show that for each k 0 there is a self-stabilizing algorithm that identi es a maximal k-dependent set, and stabilizes in O(m + n) time. An interesting by-product of our paper is the new result that in any graph there exists a set that is both maximal k-dependent and minimal (k+1)-dominat...

Funding information National Natural Science Foundation of China, Grant/Award Number: 61773081; technology transformation program of Chongqing higher education university, Grant/Award Number: KJZH17102 Summary This paper provides a time-varying feedback alternative to control of finite-time systems, which is referred to as “prescribed-time control,” exhibiting several superior features: (i) suc...

This note considers feedback stabilization of discrete-time linear time-varying systems. An operator-theoretic formulation of time-varying systems is used which allows the development to follow closely the linear time-invariant case. Using this framework, an extended Lyapunov stability result is derived. This leads to a direct proof of a feedback stabilization scheme due to Cheng without the us...

After a well starts flowing, a larger and larger portion of the reservoir contributes to production. At any given time, the radius of the portion of the reservoir that demonstrates a pressure gradient and contributes to production of fluid is the radius of drainage (ROD). The time required for the entire reservoir just to be able to contribute production is the stabilization time. Estimating th...

Finite-time stability and stabilization of retarded-type functional differential equations are developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it may appear not easily usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an...