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1

Quadratic performance analysis of switched affine time-varying systems

Li W., Huang C., Zhai G.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

429--440

EN

We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2 gain analysis problem for the switched affine time-varying systems under state feedback.

2

Positivity and stability of fractional descriptor time-varying discrete-time linear systems

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 1

5--13

EN

The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor time-varying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.

3

Positive and asymptotically stable time-varying continuous-time linear systems and electrical circuits

Kaczorek T.

Autobusy : technika, eksploatacja, systemy transportowe

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2016

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R. 17, nr 6

1362-1367

EN

The positivity and asymptotic stability of time-varying continuous-time linear systems and electrical circuits are addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of the systems and electrical circuits are established. It is shown that there exists a large class of positive and asymptotically stable electrical circuits with time-varying parameters. Examples of positive and asymptotically stable electrical circuits are presented.

PL

W pracy są analizowane zagadnienia dodatniości i stabilności asymptotycznej ciągłych układów i obwodów elektrycznych o parametrach zmiennych w czasie. Podano warunki konieczne i wystarczające dodatniości i stabilności asymptotycznej tej klasy układów i obwodów elektrycznych. Zostanie wykazane, że istnieje obszerna klasa dodatnich i stabilnych asymptotycznie obwodów elektrycznych o zmiennych parametrach. Rozważania ogólne zostaną zilustrowane przykładami obwodów elektrycznych o zmiennych w czasie parametrach.

4

A Sparse Sampling Approach to Dynamic Sub-Cycle Decomposition of Apparent Power in General Polyphase Networks

Lev-ari H., Stankovic A. M.

Przegląd Elektrotechniczny

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2015

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R. 91, nr 6

18-24

EN

We present a dynamic decomposition of apparent power in a polyphase network, based on measurements taken within a portion of a single cycle of the ac fundamental. We show that two time samples suffice for a definition that provides an attractive trade-off between computational cost and dynamic performance. The sub-cycle (or near-instantaneous) metrics that we introduce connect the time- and frequency–domain approaches in a natural way, and address the key weaknesses of the existing instantaneous decompositions. Furthermore, our power metrics are amenable to refinements via symmetrical components, thus connecting with concepts commonly used in system protection. We illustrate the sub-cycle decomposition via two polyphase examples: one of conceptual interest, the other an actual industrial voltage sag event.

PL

Przedstawiono dynamiczny rozkład mocy pozornej w obwodzie wielofazowym, oparty na pomiarach w części pojedynczego okresu harmonicznej podstawowej. Pokazano, że dwie próbki wystarczają dla defininicji, która jest atrakcyjnym kompromisem pomiędzy kosztem obliczeniowym a zachowaniem dynamicznym. Wprowadzone pod-okresowe (lub niemal-chwilowe) macierze, łączą podejście w dziedzinie czasowej z podejściem w dziedzinie częstotliwości w sposób naturalny i dotycza˛ kluczowej słabości istniejących rozkładów chwilowych. Ponadto, wprowadzone macierze mocy są podatne na uproszczenia z pomocą składowych symetrycznych, nawiązując w ten sposób do metod powszechnie stosowanych w technice zabezpieczeniowej. Rozkład pod-okresowy ilustrowany jest dwoma przykładami wielofazowymi: jeden o charakterze poznawczym i drugi dotyczący przemysłowej zapaści napięcia.

5

A new concept of filters for biomedical data processing needs

Piskorowski J.

Biocybernetics and Biomedical Engineering

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2011

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Vol. 31, no. 1

27-37

EN

This paper presents a new class of filters that can meet biomedical signal processing needs. The paper is written in a technical note style, therefore, the proposed filters are not discussed with respect to a specific problem appearing in processing of a particular biosignal. The class of filters presented in this note should be treated as a new effective tool which can be applied to many cases of biomedical signals, especially when the processing time is very important. Nevertheless, a simple example of biomedical signal filtering is presented. This paper presents a new concept of continuous-time Butterworth filters whose parameters are varied in time. Thanks to the variation of the filter parameters, the time-varying filter response is considerably faster in comparison with the traditional time-invariant filters. Therefore, we can measure and register a lot of details in the initial stage of signal duration, which is not possible in the case of traditional time-invariant filters due to their long-lasting transients. Results verifying the effectiveness of the proposed filters are presented and compared to the traditional time-invariant filter structures.

6

On Adaptive Control for the Continuous Time-varying JLQG Problem

Czornik A., Świerniak A.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 1

53-62

EN

In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated through strongly consistent estimators.

7

Stabilization of nonlinear systems: Radial optimal control approach

Sangelaji Z., Banks S.P.

Systems Science

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2003

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Vol. 29, nr 4

29-41

EN

This paper represents the optimal control of nonlinear systems based upon the associated angular approach. In the latter a general class of nonlinear systems is converted to two associated systems: a nonlinear equation on a sphere (spherical), and a radial differential system. By decoupling the two subsystems and considering only the radial system, a finite-horizon radial optimal control is designed which minimizes the radial cost function. Successive approximation technique is then introduced in which the equations are replaced by a sequence of linear, time-varying approximations. The resulting optimal control is then applied to the original angular system. This control forces the original angular system to the origin.

8

Sequential target tracking using constrained nonlinear estimators

Stubberud A.R.

Systems Science

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2003

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Vol. 29, nr 2

17-29

EN

An estimator is presented which generates sequential estimates for nonlinear, time-variable discrete-time dynamic systems in which the system state estimates are subject to an instantaneous constraint. That is, at each sample time the state estimate is constrained to lie in a given region of the state space. This nonlinear sequential estimator is an extended version of an optimal sequential estimator for linear, time-variable discrete-time systems with state estimates constrained to a given region of the state space. The linear estimator was developed from a non-probabilistic weighted linear least squares basis with the constraints added through the mechanism of Lagrange multipliers; therefore, the estimator produces "hard" constraints on the state estimate. The solution of the constrained estimation problem, at each instant of time, requires only the unconstrained state estimate at that time instant and the instantaneous constraints which define the constraint region. If the unconstrained sequential estimate satisfies the constraints, then that solution is also the constrained solution. On the other hand, if the unconstrained estimate does not satisfy the constraints, then the constrained solution is generated from the solution of a set of static equations. The constrained estimation problem is thus reduced to a sequence of nonlinear programming problems. The estimator for the state of a nonlinear system was developed by quasi-linearization of the optimal constrained linear estimator. The estimates resulting from this estimator are "optimal in the small" for nonlinear systems and are optimal for linear systems.

9

A novel multi-loop control system for highly nonlinear processes

Osypiuk R.

Systems Science

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2003

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Vol. 29, nr 4

43-54

EN

The first part of the paper deals with design and properties of a general n-loop control structure based on a divided process model. In the second part, two approaches to practical implementation of control of a two-joint serial manipulator are proposed, and simulation based verification of theoretical assumptions is carried out. The proposed multi-loop Model Following Control structure (n-MFC) may find wide application in new intelligent controllers to robust control of parameter-varying process plants.

10

A hierarchic set of characteristic equations for general linear systems

Kloet P., Neerhoff F.

Przegląd Elektrotechniczny

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2003

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R. 79, nr 10

775-778

EN

General linear single-input single-output systems are adressed. In particular, sets of characteristic equations for constant and time-varying systems are discussed. Moreover, the left and the right polynomial factorization for the Cauchy-Floquet decomposition is directly obtained.

PL

Praca dotyczy układów liniowych o jednym wejściu i jednym wyjściu, w ogólności niestacjonarnych. Przedstawia zbiór równań charakterystycznych formułowanych dla tego typu systemów. Metoda pozwala na prawo- lub lewostronną faktoryzację wielomianową dekompozycji Cauchy'ego-Floqueta.

11

Application of uncertain variables to stability analysis for a class of discrete uncertain systems

Bubnicki Z.

Systems Science

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2001

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Vol. 27, nr 1

103-110

EN

The nonlinear and time-varying uncertain system with a constant unknown vector of parameters is considered. The unknown parameter is assumed to be a value of an uncertain variable described by a certainty distribution given by an expert. The estimation of the certainty index that the system is globally asymptotically stable based on the necessary and sufficient stability conditions is proposed and considered. A simple example illustrates the approach presented.

12

The geometry of Darlington synthesis

Dewilde P.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 6

1379-1386

EN

We revisit the classical problem of `Darlington synthesis', or Darlington embedding. Although traditionally it is solved using analytic means, a more natural way to approach it is to use the geometric properties of a well-chosen Hankel map. The method yields surprising results. In the first place, it allows us to formulate necessary and sufficient conditions for the existence of the embedding in terms of systems properties of the transfer operation to be embedded. In addition, the approach allows us to extend the solution to situations where no analytical transform is available. The paper has a high review content, as all the results presented have been obtained during the last twenty years and have been published. However, we make a systematic attempt at formulating them in a geometric way, independent of an accidental parametrization. The benefit is clarity and generality.

13

Szego's First Limit Theorem in Terms of a Realization of a Continuous-Time Time-Varying System

Iglesias P. A., Zang G.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 6

1261-1276

EN

It is shown that the limit in an abstract version of Szego's limit theorem can be expressed in terms of the antistable dynamics of the system. When the system dynamics are regular, it is shown that the limit equals the difference between the antistable Lyapunov exponents of the system and those of its inverse. In the general case, the elements of the dichotomy spectrum give lower and upper bounds.