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1

Assignability of numerical characteristics of time-varying systems

Babiarz A., Czornik A., Klamka J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 6

1007--1022

EN

The main aim of this article is to survey and discuss the existing state of art concerning the assignability by a feedback of numerical characteristics of linear continuous and discrete time-varying systems. Most of the results present necessary or sufficient conditions for different formulation of the Lyapunov spectrum assignability problem. These conditions are expressed in terms of various controllability types and optimalizability of the controlled systems and certain properties of the free system such as: regularity, diagonalizability, boundness away, integral separation and reducibility.

2

Interval state estimation for linear time-varying (LTV) discrete-time systems subject to component faults and uncertainties

Khan Awais, Xie Wei, Zhang Langwen, Ihsanullah

Archives of Control Sciences

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2019

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Vol. 29, No. 2

289--305

EN

This paper deals with the design of an interval state estimator for linear time-varying (LTV) discrete-time systems subject to component faults and uncertainties. These component faults and uncertainties are assumed to be unknown but bounded without giving any other information, whose effect can be approximated using these bounds. In the first part of this work, an interval state estimator for such systems is designed to deal with these component faults and uncertainties. The result is then extended to find an interval state estimator for a noncooperative LTV discrete-time system subject to component faults and uncertainties by similarity transformation of coordinates. The proposed interval state estimator guaranteed bounds on the observed states that are consistent with the system states. The observer convergence is also ensured. The designed method is simple and easy to be implemented. Two numerical examples are given to show the effectiveness of the proposed method.

3

Filter network of dynamic nonstationary elements

Kaszyński R., Sztandera A., Wiechetek K.

Przegląd Elektrotechniczny

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2016

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R. 92, nr 11

119--123

EN

In this paper a concept of creating fast nonstationary filters based on 1-st order high-pass and low-pass elements with time-varying parameters is presented. Implementing time-varying parameters in the form of gain function and time function enables shortening of the transient state, which results in their high utility in creation of complex filter structures. Computer simulation and research on these selected structures were conducted with previously established frequency characteristics.

PL

W artykule przedstawiono koncepcję tworzenia szybkich filtrów niestacjonarnych z elementów I-go rzędu o zmiennych parametrach, które są elementami dolnoprzepustowymi i górnoprzepustowymi. Wprowadzone zmienne w czasie parametry w postaci funkcji wzmocnienia i funkcji czasowych pozwoliły wielokrotnie skrócić stany nieustalone, co spowodowało ich dużą przydatność w tworzeniu rozbudowanych struktur filtrów. Przeprowadzono badania symulacyjne struktur o wybranych, z góry założonych właściwościach częstotliwościowych.

4

Wyznaczanie macierzy przekształceń zmiennych stanu liniowych układów o zmiennych parametrach

Kaczorek T.

Pomiary Automatyka Kontrola

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2005

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R. 51, nr 7-8

12-15

PL

Podano metodę wyznaczania macierzy przekształcającej sterowalną parę macierzy liniowych ukałdów ciągłych i dyskretnych o zmiennych parametrach o jednym wejściu do zadanej postaci kanonicznej. Sformułowano warunki przy spełnieniu których macierz A(t) układu wyjściowego i przekształconego A(t) mają ten sam wielomian charakterystyczny, czyli det[Is-A(t)]. Podano dwie procedury wyznaczania tej macierzy, które zilustrowano przykładami.

EN

A method is proposed for determination of state transformation of a pair of matrices to given canonical form for linear time-varying continuous-time and discrete-time single input systems. Conditions are established under which the given matrix A(t) and the transformated matrix A(t) have the same characteristic polynomial, i.e. det[Is-A(t) = det[Is-A(t)]. Two procedures for determination of the transformation matrix are gives and illustrated by examples.

5

Adaptive state feedback control for a class of linear systems with unknown bounds of uncertainties.

Fenlin L., Hao W., Qingxian W., Mingwu S., Siying Z.

Systems Science

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2001

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Vol. 27, nr 3

23-34

EN

The problem of adaptive robust stabilization for a class of linear time-varying systems with disturbance and nonlinear uncertainties is considered. The bounds of the disturbance and uncertainties are assumed to be unknown, being even arbitrary. For such uncertain dynamical systems, the adaptive robust state feedback controller is obtained. And the resulting closed-loop systems are asymptotically stable in theory. Moreover, an adaptive robust state feedback control scheme is given. The scheme ensures the closed-loop systems exponentially practically stable and can be used in practical engineering. Finally, simulations show that the control scheme is effective.