Related papers: Consistent systems of linear differential and diff…
We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like…
In this paper we present how spectral properties of certain linear operators vary when operators are considered in different Hilbert spaces having common dense domain as the space of polynomials in one real variable with complex…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
This paper investigates the controllability of systems governed by conformable fractional order derivatives. It first establishes the existence and uniqueness of evolution operators for non-autonomous fractional-order homogeneous systems,…
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
We consider characterisations of unitary dilations and approximations of irreversible classical dynamical systems on a Hilbert space. In the commutative case, building on the work in [9], one can express well known approximants (e.g. Hille-…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…
This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers.…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…
We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive…
Continuous linear dynamical systems are used extensively in mathematics, computer science, physics, and engineering to model the evolution of a system over time. A central technique for certifying safety properties of such systems is by…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
We study point and higher symmetries for the hydrodynamic-type systems with two independent variables $t$ and $x$ with and without explicit dependence of the equations on $t,x$. We consider those systems which possess an…
We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t),…
The classical Hormander's inequality for linear partial differential operators with constant coeffcients is extended to pseudodifferential operators.
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…