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A multi-dimensional switched system or multi-mode multi-dimensional ($M^3D$) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the $M^3D$ system, whose state transitions at…
Determining the number of stable phase-locked solutions for locally coupled Kuramoto models is a long-standing mathematical problem with important implications in biology, condensed matter physics and electrical engineering among others. We…
In this paper, from the structural perspective, we propose a new stability analysis approach for the consensus of linear multi-agent systems. Different from the general tools: the Laplacian matrix based method and the Lyapunov's method,…
Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…
Partial integrability in phase-oscillator dynamics is typically examined for identically connected oscillators or groups thereof. Yet, the precise connectivity conditions that ensure conserved quantities on general networks remain unclear.…
We study dynamics of a bimodal planar linear switched system with a Hurwitz stable and an unstable subsystem. For given \textit{flee time} from the unstable subsystem, the goal is to find corresponding \textit{dwell time} in the Hurwitz…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…
This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…
In this paper we study the controllability of networked systems with static network topologies using tools from algebraic graph theory. Each agent in the network acts in a decentralized fashion by updating its state in accordance with a…
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…
We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be different in general. By developing a…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…
Synchronization processes in populations of identical networked oscillators are in the focus of intense studies in physical, biological, technological and social systems. Here we analyze the stability of the synchronization of a network of…
This paper addresses the problem of navigation control of a general class of uncertain nonlinear multi-agent systems in a bounded workspace of $\mathbb{R}^n$ with static obstacles. In particular, we propose a decentralized control protocol…
Multi-agent ergodic coverage via Spectral Multiscale Coverage (SMC) provides a principled framework for driving a team of agents so that their collective time-averaged trajectories match a prescribed spatial distribution. While classical…