arXiv subjects

Grigory Sklyar

Publications and source records attributed to Grigory Sklyar.

4 recordsLinked to original sources

arXiv2021

Implementation of the algorithm for constructing homogeneous approximations of nonlinear control systems

We present a 'calculator' for constructing a homogeneous approximation of nonlinear control systems, which is based on the algebraic approach developed by the authors in their previous papers. This approach mainly uses linear algebraic and combinatorial tools, so, it is perfectly adapted to computer realization. We describe the algorithm and discuss its capabilities and limitations. We present its implementation as a web application and show by example how this app works.

math.OC↗

arXiv2019

Conditions of exact null controllability and the problem of complete stabilizability for time-delay systems

For a class of linear time-delay control systems satisfying the property of completability of the generalized eigenvectors we prove that the problems of complete stabilizability and exact null controllability are equivalent.

math.OC↗

arXiv2017

Exact null controllability, complete stabilizability and exact final observability: the case of neutral type systems

For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We extend this result to the case when the feedback is not bounded. This enables the characterization of exact null controllability and complete stabilizability for neutral type systems. By duality, we obtain a result about continuous final observability.Illustrative examples are given.

math.OC↗

arXiv2015

Exact observability and controllability for linear neutral type systems

The problem of exact observability is analyzed for a wide class of neutral type systems by an infinite dimensional approach. The duality with the exact controllabil-ity problem is the main tool. It is based on an explicit expression of a neutral type system which corresponding to the abstract adjoint system. A nontrivial relation is obtained between the initial neutral system and the system obtained via the adjoint abstract state operator. The characterization of the duality between controllability and observability is deduced, and then observability conditions are obtained.

math.OC↗