Oscillations in lossless propagation models: a Liapunov-Krasovskii approach

Râsvan, Vladimir

doi:10.1093/imamci/19.1_and_2.157

Cited by 76 publications

(43 citation statements)

References 12 publications

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“…The inequalities (26) and (27) can be shown to be equivalent to (18) and (19) by eliminating U using Proposition 2 in [3]. From the above, we can conclude the following.…”

Section: Discretization Of Lkfmentioning

confidence: 65%

“…Such equations initially described by a hyperbolic type of partial differential equations can be written as coupled differential-difference equations by integrating along the characteristics [19]. As many such PDEs represent lossless propagation systems [1] [11], the resulting coupled differential-difference equations are often known as the lossless propagation model [18] [20]. For the stability analysis of the systems, while some early works tend to transform them into the standard functional differential equations of neutral type [15], many more recent works prefer to treat them directly [16] [17].…”

Section: Introductionmentioning

confidence: 99%

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Stability of coupled differential-functional equations with discrete and distributed delays via discretized LKF method

2011

2011 Chinese Control and Decision Conference (CCDC)

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This article discusses the Lyapunov-Krasovskii functional (LKF) method for the stability problem of coupled differential-functional equations with distributed delays and one discrete delay. Discretization is used to render the stability conditions of an LMI form for the systems. The conclusion may be easily extended to deal with the stability problem of systems with either distributed delays and multiple commensurate discrete delays or mix delays. Finally, the numerical examples is presented to illustrate the effectiveness of the method.

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“…The inequalities (26) and (27) can be shown to be equivalent to (18) and (19) by eliminating U using Proposition 2 in [3]. From the above, we can conclude the following.…”

Section: Discretization Of Lkfmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Stability of coupled differential-functional equations with discrete and distributed delays via discretized LKF method

2011

2011 Chinese Control and Decision Conference (CCDC)

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“…Starting from the aforementioned problems and from (Cooke and Krumme (1968), Cooke (1970)) a methodology has been elaborated for solving the lossless propagation problems with (possibly) derivative boundary conditions occurring in thermal, hydraulic and electrical engineering (Rȃsvan (1975a)); this methodology has been presented in several papers along the last decades (Rȃsvan (1981(Rȃsvan ( , 1984(Rȃsvan ( , 1998(Rȃsvan ( , 2000, Rȃsvan and Niculescu (2002), Rȃsvan (2006Rȃsvan ( , 2009aRȃsvan ( ,b, 2012). Further development and new applications to flexible manipulator control, overhead cranes and marine risers as well as to oilwell drillstrings dynamics may be found in (Rȃsvan (2014)).…”

Section: Overview and State Of The Artmentioning

confidence: 99%

From conservation laws to wave propagation and back -dynamics and control in combined heat/electricity generation∗∗The research has been supported by the Project UEFISCDI-ROMANIA PN-II-ID.

Râsvan

2015

IFAC-PapersOnLine

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Starting from some pioneering papers in distributed parameter control systems for steam turbines and their auxiliaries, a bilinear model for steam turbines with steam extraction and "long" steam pipes was elaborated and the feedback control synthesis has been performed using a suitable control Liapunov functional of quadratic type, both for distributed parameters systems and their lumped parameter approximation. The synthesized control ensures global stabilization of the steady state solution. It has been observed much later that the linearized steam wave propagation equations underlying the model were in fact a simplified linearized version of the conservation laws of the isentropic flow. Following this remark and bearing in mind the recent advances in the control of the systems described by conservation laws, the model of the combined heat electricity generation is re-written as a system which is linear in control; consequently the feedback stabilization also requires re-examination.In 1946 an entire issue of an engineering journal was dedicated to the problem of the stability of some linearized feedback control systems in power engineering: it contained 3 papers written by two authors -an engineer and a mathematician -apparently before the war from where they did not return (Sokolov (1946), Kabakov (1946, Kabakov and Sokolov (1946)). Almost at the same time there were published other three papers on the same subject (Solodovnikov (1941), Aronovich (1948), Neimark (1948). The first ones dealt with thermal power engineering while the second ones with hydraulic power engineering. Nevertheless the approach had been the same -as the title of (Solodovnikov (1941)) says -the application of the Laplace transform and obtaining some characteristic equation whose roots needed to be localized in the left half plane of C. Later some of their models and results were integrated in monographs e.g. (Lurie (1950), Popov (1954) and the subsequent research followed.The examination of the mathematical models of the aforementioned papers indicates that they are based on similar models: the models contained the linear wave equation without losses describing lossless propagation of steam or water over long pipes or galleries. The dynamics of the power devices -water or steam turbines -were oversimplified, described by linear ordinary differential equations like the control structure based on the mechanical controllers and sensors of that time. A special mention has to be nevertheless made for (Kabakov (1946)) where the deduction of the model starts from the hyperbolic partial differential equations of the isentropic flow which are nonlinear; they are however linearized from the very beginning ⋆ The research has been supported by the Project UEFISCDI-ROMANIA PN-II-ID .(and with some omission) but the starting point is useful to be known.The models have been "re-discovered" due to the fact that the characteristic equations involved there contained terms of the form e −τs thus pointing to some possibly associated equations with delayed ...

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“…Theorem 3 implies that the controls (34) ensure that all trajectories of (25) track the reference trajectory. Moreover, given any velocity control set [v a , v b ] with positive constants v a and v b , and any constant µ > 0 such that v a + µ ≤ v cr (t) ≤ v b − µ for all t ∈ R, we can choose small enough so that v a ≤ v c (t) ≤ v b for all t ∈ R to satisfy input constraints, and similarly for θ c .…”

Section: Application To Uav Dynamicsmentioning

confidence: 99%

“…See for example [2], [3], [11], [13], [31]- [34], [38] for discussions on the many advantages of Lyapunov-Krasovskii functionals, e.g., for inverse optimality or quantifying the robustness of controllers to uncertainty. There are also predictive methods that allow time-varying input delays [15], and prediction can be used to compensate arbitrarily long time delays.…”

Section: Introductionmentioning

confidence: 99%

Stabilization for feedforward systems with delay in the input

Mazenc

Malisoff

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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We solve a family of uniform global asymptotic stabilization problems for time varying feedforward systems with a delayed input. Our solution relies on a time-varying change of coordinates and Lyapunov-Krasovskii functionals. It applies under any given constant delay, and provides controllers of arbitrarily small amplitude. We also prove input-to-state stability with respect to additive disturbances on the controllers under certain bounds on the disturbances. We demonstrate our work using a tracking problem for a model that is suitable for high level formation flight of unmanned air vehicles.

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Oscillations in lossless propagation models: a Liapunov-Krasovskii approach

Cited by 76 publications

References 12 publications

Stability of coupled differential-functional equations with discrete and distributed delays via discretized LKF method

Stability of coupled differential-functional equations with discrete and distributed delays via discretized LKF method

From conservation laws to wave propagation and back -dynamics and control in combined heat/electricity generation∗∗The research has been supported by the Project UEFISCDI-ROMANIA PN-II-ID.

Stabilization for feedforward systems with delay in the input

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