Related papers: On local linearization of control systems

This paper is motivated by the problem of asymptotically stabilizing invariant sets in the state space of control systems by means of output feedback. The sets considered are smooth embedded in submanifolds and the class of system is…

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…

We consider nonlinear scalar-input differential control systems in the vicinity of an equilibrium. When the linearized system at the equilibrium is controllable, the nonlinear system is smoothly small-time locally controllable, i.e.,…

While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…

The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…

By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…

We consider a problem of optimal distribution of conductivities in a system governed by a non-local diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel…

This paper presents conditions for establishing topological controllability in undirected networks of diffusively coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our…

This paper considers the problem of controlled invariance of involutive regular distribution, both for smooth and real analytic cases. After a review of some existing work, a precise formulation of the problem of local and global controlled…

In this paper, we study linear control systems with positive bounded orbits. We show that the existence of positive bounded orbits imposes strong algebraic and topological constraints on the state space. In fact, a linear control system has…

For linear control systems with bounded control range, the state space is compactified using the Poincar\'e sphere. The linearization of the induced control flow allows the construction of invariant manifolds on the sphere and of…

The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time…

Local asymptotic stabilizability is a topic of great theoretical interest and practical importance. Broadly, if a system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, we are guaranteed a feedback controller $u(x)$ that forces…

The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the…

The critical loci of a map $f:X\to Y$ between smooth schemes over a field $k$ are the locally closed subschemes $\Sigma^i(f)\subseteq X$ where the differential of $f$ has constant rank. We prove that if $f : X\to \mathbb A^r$ is the general…

Linear observed systems on manifolds are a special class of nonlinear systems whose state spaces are smooth manifolds but possess properties similar to linear systems. Such properties can be characterized by preintegration and exact…

Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…

We consider infinitely renormalizable unimodal mappings with topological type which is periodic under renormalization. We study the limiting behavior of fixed points of the renormalization operator as the order of the critical point…

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…