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This paper presents a first-order {distributed continuous-time algorithm} for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size,…

In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…

The leader-following consensus problem for general linear multi-agent systems over jointly connected switching networks has been a challenging problem and the solvability of the problem has been limited to the class of linear multi-agent…

We deal with algorithmic techniques for minimal cost input-connectivity while maintaining controllability of linear systems. The input matrix is assumed to be constrained in the sense that the set of states that each input (if present) can…

Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has…

In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…

Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…

In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness.…

We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…

We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…

Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…

Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…

Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…

This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the…

Information-theoretic arguments focus on modeling the reliability of information transmission, assuming availability of infinite data at sources, thus ignoring randomness in message generation times at the respective sources. However, in…

We introduce a new, "worst-case" model for an asynchronous communication network and investigate the simplest (yet central) task in this model, namely the feasibility of end-to-end routing. Motivated by the question of how successful a…

This paper investigates the minimal number of inputs/outputs required to guarantees the controllability/observability of a system, under the condition that its state transition matrix (STM) is prescribed. It has been proved that this…

This paper studies the graph-theoretic conditions for stability of positive monotone systems. Using concepts from input-to-state stability and network small-gain theory, we first establish necessary and sufficient conditions for the…