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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

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.

3

Quantitative Lp stability analysis of a class of linear time-varying feedback systems

Gurfil P.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 2

179-184

EN

The Lp stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for Lp stability, with 1LpL Y, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a single pole at the origin, the upper bound on the output-to-input ratio is constant. Thus, an explicit closed-form calculation of this bound for some simple particular case provides a powerful generalization for the more complex cases. The importance of the results is illustrated by an example taken from missile guidance theory.

4

Locally Positive Nonlinear Systems

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 4

505-509

EN

The notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positiveness of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced, and sufficient conditions for local reachability in the direction of a cone of this class of nonlinear systems are presented.

5

On the discrete time-varying JLQG problem

Czornik A., Świerniak A.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 2

203-207

EN

In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.