Related papers: Topological equivalence canonical forms for linear…
This paper is devoted to a study of linear, differential and topological classifications for linear controlled systems governed by ordinary differential equations. The necessary and sufficient conditions for the linear and topological…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with…
The paper continues the authors' study of the linearizability problem for nonlinear control systems. In the recent work [K. Sklyar, Systems Control Lett. 134 (2019), 104572], conditions on mappability of a nonlinear control system to a…
We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control…
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…
We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…
An observable canonical form is formulated for the set of rational systems on a variety each of which is a single-input-single-output, affine in the input, and a minimal realization of its response map. The equivalence relation for the…
This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
The paper deals with the observer design problem for a wide class of triangular time-varying nonlinear systems, with unobservable linearization. Sufficient conditions are derived for the existence of a Luenberger-type observer, when it is a…
The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
The following numerical control over the topological equivalence is proved: two complex polynomials in $n\not= 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of…
A new finite atlas of overlapping balanced canonical forms for multivariate discrete-time lossless systems is presented. The canonical forms have the property that the controllability matrix is positive upper triangular up to a suitable…
In this note we consider continuous-time systems x'(t) = A(t) x(t) + B(t) u(t), y(t) = C(t) x(t) + D(t) u(t), as well as discrete-time systems x(t+1) = A(t) x(t) + B(t) u(t), y(t) = C(t) x(t) + D(t) u(t) whose coefficient matrices A, B, C…