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The algebraic structure of delay-differential systems: a behavioral perspective

Heide Glüsing-Lüerssen, Paolo Vettori, Sandro Zampieri (2001)

Kybernetika

This paper presents a survey on the recent contributions to linear time- invariant delay-differential systems in the behavioral approach. In this survey both systems with commensurate and with noncommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for systems with commensurate delays, this is not the case for systems with noncommensurate delays. In the...

The anti-disturbance property of a closed-loop system of 1-d wave equation with boundary control matched disturbance

Xiao-Rui Wang, Gen-Qi Xu (2019)

Applications of Mathematics

We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the...

The choice of the forms of Lyapunov functions for a positive 2D Roesser model

Tadeusz Kaczorek (2007)

International Journal of Applied Mathematics and Computer Science

The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix A^{T}PA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.

The Frisch scheme in algebraic and dynamic identification problems

Roberto P. Guidorzi, Roberto Diversi, Umberto Soverini (2008)

Kybernetika

This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension...

The steady-state impedance operator of a Linear Periodically Time-Varying one-port network and its determination

Radosław Kłosiński (2009)

International Journal of Applied Mathematics and Computer Science

The main subject of the paper is the description and determination of the impedance operator of a linear periodically timevarying (LPTV) one-port network in the steady-state. If the one-port network parameters and the supply vary periodically with the same period, the network reaches a periodic steady state. However, the sinusoidal supply may induce a nonsinusoidal voltage or current. It is impossible to describe such a phenomenon by means of one complex number. A periodically time-varying one-port...

The technique of splitting operators in perturbation control theory

Michail M. Konstantinov, Petko Hr. Petkov, Nikolaĭ D. Hristov (2005)

Kybernetika

The paper presents the technique of splitting operators, intended for perturbation analysis of control problems involving unitary matrices. Combined with the technique of Lyapunov majorants and the application of the Banach or Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the general feedback synthesis problem, and the pole assignment...

Topology design for group consensus in directed multi-agent systems

Onur Cihan (2020)

Kybernetika

In this paper, we investigate the grouping behavior of multi-agent systems by exploiting the graph structure. We propose a novel algorithm for designing a network from scratch which yields the desired grouping in a network of agents utilizing a consensus-based algorithm. The proposed algorithm is shown to be optimal in the sense that it consists of the minimum number of links. Furthermore, we examine the effect of adding new vertices and edges to the network on the number of groups formed in the...

Transfer function equivalence of feedback/feedforward compensators

Vladimír Kučera (1998)

Kybernetika

Equivalence of several feedback and/or feedforward compensation schemes in linear systems is investigated. The classes of compensators that are realizable using static or dynamic, state or output feedback are characterized. Stability of the compensated system is studied. Applications to model matching are included.

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