Related papers: On local linearization of control systems
In this paper we extend the results on controllability of linear systems obtained in "Controllability of linear systems on solvable Lie groups", from solvable Lie groups to Lie groups with finite semisimple center.
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…
We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie…
(Completely regular) locales generalize (Tychonoff) spaces; indeed, the passage from a locale to its spatial sublocale is a well understood coreflection. But a locale also possesses an equally important pointless sublocale, and with…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
Spatially resolved local quantum geometric markers play a crucial role in the diagnosis of topological phases without long-range translational symmetry, including amorphous systems. Here, we focus on the nonlocality of such markers. We…
A general ansatz in Renormalization Theory, already established in many important situations, states that exponential convergence of renormalization orbits implies that topological conjugacies are actually smooth (when restricted to the…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
A result on $C^0$ linearization which is differentiable at the hyperbolic fixed point is known. In this paper, we further investigate a partially hyperbolic diffeomorphism $F$ to find a local $C^0$ conjugacy, which is $C^1$ on the center…
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…
The propagation path of topologically protected states is bound to the interface between regions with different topology, and as such, the functionality of linear photonic devices leveraging these states is fixed during fabrication. Here,…
This paper considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different…
In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space.…
We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…
We consider smooth, complex quasi-projective varieties $U$ which admit a compactification with a boundary which is an arrangement of smooth algebraic hypersurfaces. If the hypersurfaces intersect locally like hyperplanes, and the relative…