Stability and controllability of switched systems

Klamka, Jerzy; Czornik, Adam; Niezabitowski, Michał

doi:10.2478/bpasts-2013-0055

Cited by 52 publications

(33 citation statements)

References 69 publications

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“…However, one advantage is that these computations need to be performed only once for all integers k ≤ k max and a selected h max , and the results can be saved for later use. The formulation of any nonlinear dependency collection: (27) and other operations that could be required during the solution process (such as differentiation during Jacobian matrix evaluations) do not introduce much numerical weight for efficient symbolic computation implementations [49]. The dependencies in each f NL (w) can be used when addressing N(w) in (23).…”

Section: Symbolic Computation Approachmentioning

confidence: 99%

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

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This paper discusses the ability to obtain periodic steady-state solutions for fractional nonlinear circuit problems. For a class of nonlinear problems with fractional derivatives (based on the Caputo or Riemann-Liouville definitions), a methodology is proposed to derive equations representing the dependencies between the harmonics of the sought variables. Two approaches are considered for how to address the apparent nonlinear dependencies: one based on symbolic computation and the other a numerical approach based on the analysis of time functions. An example problem with fractional and nonlinear elements is presented to illustrate the usefulness of the proposed methodology. Two error criteria are introduced to verify the accuracy of the obtained results. The methodology is mainly designed to provide referential solutions in analyses of the numerical method called SubIval (the subinterval-based method for computation of the fractional derivative in initial value problems).

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Section: Symbolic Computation Approachmentioning

confidence: 99%

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

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“…We also model the behavior of TCP/UDP/XCP mixed traffic. Our fluid flow model is a type of switched system [36]. We extended the fluid-flow model that considered the impact of the UDP traffic on the stability of the bottleneck network.…”

Section: Fluid Flow Approximation Of Time-limited Tcp/udp/xcp Streamsmentioning

confidence: 99%

Fluid flow approximation of time-limited TCP/UDP/XCP streams

Domańska¹,

Domański²,

Czachórski³

et al. 2014

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. This article presents the use of fluid flow approximation to model interactions between a set of TCP, UDP and XCP flows in the environment of IP routers using AQM (Active Queue Management) algorithms to control traffic congestion. In contrast to other works, independent UDP and TCP streams are considered and the model allows to start and end data transmissions in TCP, UDP and XCP streams at any time moment. It incorporates several Active Queue Management mechanisms: RED, NLRED, CHOKe.

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“…where g and Ω are called generator vector and fundamental matrix, respectively, which can be determined recursively for r inputs w 1 , w 2 , ..., w r according to (6) through assuming the initial generator g 0 = 1 and fundamental matrix Ω 0 = 1:…”

Section: P1-ts Fuzzy Scheduling Control Schemementioning

confidence: 99%

“…The gain scheduling design is frequently an iterative process, based on the series expansion linearization of a system about its equilibrium points at which a family of local linear controllers is determined to satisfy the system robustness. The survey of scheduled control synthesis is presented in [1,2], however, the effectiveness of a gain scheduling control system is still the subject of attention in the recent works [3][4][5][6]. The numerous research works demonstrate the usefulness of a fuzzy scheduled based control in different applications [7][8][9], developed especially based on the Takagi-Sugeno (TS) model [10].…”

Section: Introductionmentioning

confidence: 99%

P1-TS fuzzy scheduling control system design using local pole placement and interval analysis

Smoczek¹

2014

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The linear parameter-varying (LPV) discrete-time model based design of a fuzzy scheduling control scheme is developed through incorporating the advantages of P1-TS theory, and applying the local pole placement method and interval analysis of closed-loop system polynomial coefficients. The synthesis of fuzzy scheduling control scheme is proposed in the form of iterative procedure, which enables to find the appropriate number of intervals of a fuzzy interpolator ensuring that a family of local linear controllers places closed-loop polynomial coefficients within a desired range. The computational complexity of multidimensional fuzzy scheduling control scheme synthesis is reduced using a fundamental matrix method and recursive procedure for fuzzy rule-based interpretation. The usability of the proposed method is illustrated by an implementation example and experimental results obtained on a laboratory scaled overhead crane.

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Stability and controllability of switched systems

Cited by 52 publications

References 69 publications

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Fluid flow approximation of time-limited TCP/UDP/XCP streams

P1-TS fuzzy scheduling control system design using local pole placement and interval analysis

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