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On one algorithm for solving the problem of source function reconstruction

Vyacheslav Maksimov (2010)

International Journal of Applied Mathematics and Computer Science

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations...

On robust stability of neutral systems

Silviu-Iulian Niculescu (2001)

Kybernetika

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.

On some relaxations commonly used in the study of linear systems

Olivier Bachelier, Driss Mehdi (2015)

Kybernetika

This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis...

On stable cones of polynomials via reduced Routh parameters

Ülo Nurges, Juri Belikov, Igor Artemchuk (2016)

Kybernetika

A problem of inner convex approximation of a stability domain for continuous-time linear systems is addressed in the paper. A constructive procedure for generating stable cones in the polynomial coefficient space is explained. The main idea is based on a construction of so-called Routh stable line segments (half-lines) starting from a given stable point. These lines (Routh rays) represent edges of the corresponding Routh subcones that form (possibly after truncation) a polyhedral (truncated) Routh...

On the constrained controllability of dynamical systems with multiple delays in the state

Beata Sikora (2003)

International Journal of Applied Mathematics and Computer Science

Linear stationary dynamical systems with multiple constant delays in the state are studied. Their relative and approximate controllability properties with constrained controls are discussed. Definitions of various types of controllability with constrained controls for systems with delays in the state are introduced. Some theorems concerning the relative and the approximate relative controllability with constrained controls for dynamical systems with delays in the state are established. Various types...

On the regulator problem for a class of LTI systems with delays

Bernardino Castillo-Toledo, Eduardo Núñez-Pérez (2003)

Kybernetika

This paper deals with the problem of tracking a reference signal while maintaining the stability of the closed loop system for linear time invariant systems with delays in the states. We show that conditions for the existence of a solution to this problem (the so-called regulation problem), similar to those known for the case of delay-free linear systems, may be given. We propose a solution for both the state and error feedback regulation.

On the structure at infinity of linear delay systems with application to the disturbance decoupling problem

Rabah Rabah, Michel Malabre (1999)

Kybernetika

The disturbance decoupling problem is studied for linear delay systems. The structural approach is used to design a decoupling precompensator. The realization of the given precompensator by static state feedback is studied. Using various structural and geometric tools, a detailed description of the feedback is given, in particular, derivative of the delayed disturbance can be needed in the realization of the precompensator.

Currently displaying 241 – 260 of 421