Shaheed N. Huseen · 2010
In this paper, we give a new bounds for Lyapunov function and we state a new hypothesis depending on Lyapunov function for establishing two types of stability which are exponential stability and uniform exponential stability for nonlinear systems. ــرارـقتــسلأا ة لأا س ةـ و ــرارـقتــسلأا ة لأأ س ةــمظتنملا ةـ ةــطـخلالا ةـمـظنلأل نسح رصان دهش مولعلا ةلك / راق يذ ةعماج تابساحلا مولع مسق ةصلاخلا تاـضرـف انعـضو كـلذـك فوــناباــل ةــلادـل هدـدـج دوــق ءاطـعإـب ثـحبلا اذـه ف انمـق تـعت فوـناباـل ةــلاد ىلع دـمـ و ةـــسلأا ةــرارـقتـسلأا امـه ةرارـقـتــسلاا نم نــعوـن ىلع لوـصحـلل .ةــطـخلالا ةمظنلأل ةمظتنملا ةـــسلأا ةــرارـقتـسلأا
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Luo Yuehu, Dexing Feng · Journal of Mathematical Analysis and Applications · 1998
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Abed Bounemoura, Jean-pierre Marco · 2016
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Vasile Drǎgan, Toader Morozan, Adrian‐Mihail Stoica · 2009
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August A. Balkema, Claudia Klüppelberg, Sidney I. Resnick · 2000
A random vector X generates a natural exponential family of vectors X , 2 , where is the set where the moment generating function (mgf) K() = Ee X is finite. Assume that is open and X non-degenerate. Suppose there exist affine transformations ff (x) = A x+a depending continuously on the parameter and a non-degenerate vector Y so that ff \\Gamma1 (X ) ) Y when diverges. In this paper it will be shown that the limit vector satisfies a stability relation. Some examples of this limit relation are presented. AMS Subject Classifications: Primary 60F05; secondary 60E05,44A10 Keywords: Esscher, exponential family, Laplace transform, multivariate, stability Author for correspondence. 1 1 Introduction Exponential group families are of special interest to statisticians. Recently there has also been interest in this subject from the quarter of mathematical physics. The book Faraut and Kor'anyi [1994] gives a complete classification of all exponential families which are ge...
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Abed Bounemoura · 2010
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Oran Gannot · IMA Journal of Mathematical Control and Information · 2022
Abstract We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on Popov’s hyperstability theorem. The main results are new bounds on convergence rates for perturbations of the damped harmonic oscillator, including the Hessian-damped case, when the perturbations satisfy certain sectoriality or convexity hypotheses. We also include a simplified proof of Popov’s theorem in its general form, which has the virtue that it often applies at the margins of stability when other criteria typically degenerate.
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G. Grammel, I. Maizurna · Journal of Mathematical Analysis and Applications · 2003
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Xin Wang, Yu Xue, Yantao Wang et al. · Intelligent control and learning systems · 2025
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Jonathan Goodman, Albert Greenberg, Neal Madras et al. · Journal of the ACM · 1988
Binary exponential backoff is a randomized protocol for regulating transmissions on a multiple-access broadcast channel. Ethernet, a local-area network, is built upon this protocol. The fundamental theoretical issue is stability: Does the backlog of packets awaiting transmission remain bounded in time, provided the rates of new packet arrivals are small enough? It is assumed n ≥ 2 stations share the channel, each having an infinite buffer where packets accumulate while the station attempts to transmit the first from the buffer. Here, it is established that binary exponential backoff is stable if the sum of the arrival rates is sufficiently small. Detailed results are obtained on which rates lead to stability when n = 2 stations share the channel. In passing, several other results are derived bearing on the efficiency of the conflict resolution process. Simulation results are reported that, in particular, indicate alternative retransmission protocols can significantly improve performance.
Cited by 173Open access
Omkar Sudhir Patil, Axton Isaly, Bin Xian et al. · IEEE Control Systems Letters · 2021
A class of continuous robust controllers termed Robust Integral of the Sign of the Error (RISE) have been published over the past two decades as a means to yield asymptotic tracking error convergence and asymptotic identification of time-varying uncertainties, for classes of nonlinear systems that are subject to sufficiently smooth bounded exogenous disturbances and/or modeling uncertainties. Despite the wide application of RISE-based techniques, an open question that has eluded researchers during this time-span is whether the asymptotic tracking error convergence is also uniform or exponential. This question has remained open due to certain limitations in the traditional construction of a Lyapunov function for RISE-based error systems. In this letter, new insights on the construction of a Lyapunov function are used that result in an exponential stability result for RISE-based controllers. As an outcome of this breakthrough, the inherent learning capability of RISE-based controllers is shown to yield exponential identification of state-dependent disturbances/uncertainty.
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Vincent Andrieu, Bayu Jayawardhana, Laurent Praly · IEEE Transactions on Automatic Control · 2016
We investigate how the following properties are related to each other: i) A manifold is “transversally” exponentially stable; ii) the “transverse” linearization along any solution in the manifold is exponentially stable; and iii) there exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property.
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Hélène Barucq, Mathieu Fontes · 2007
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Albert G. Greenberg, See Profile, See Profile et al. · 1988
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Poulin, Joseph · UWSpace (University of Waterloo) · 2024
The control of electromagnetic systems, which is governed by Maxwell's equations, is of interest for various reasons such as controlling plasma in a nuclear fusion reactor or magnetically trapping antiparticles for observation. Proving that a controlled system is exponentially stable is of particular interest, as exponential stability infers that the system will converge asymptotically to a steady state solution. A tool called the multiplier method is considered, which allows for exponential stability to be demonstrated by defining an auxiliary functional and proving it is bounded by the system energy and the energy's time derivative in a particular way. If an appropriate bound is shown, exponential stability is not only guaranteed, but the exponential function which bounds the L2 norm of the system variables will be fully determined in terms of the systems parameters. Currently, there is ongoing work into generalizing the multiplier method approach for a class of problems known as Port-Hamiltonian systems. This thesis aims to contribute to this work by formulating Maxwell's equations as a Port-Hamiltonian system, and using this formulation as a basis for determining how to choose the auxiliary functional needed in the multiplier method.
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Dan Radu, Petre Preda · 2015
Abstract. The aim of this paper is to give some sufficient, respectively necessary and sufficient conditions, for the exponential stability of evolu-tion operators in infinite-dimensional spaces. The obtained results are like those, of Datko-type, for evolutionary processes which are linear operators-valued. 1.
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И. Д. Коструб, А. И. Перов · Mathematical Notes · 2023
Using the theory of commutative Banach algebras, we find an estimate of the solution of a higher-order linear differential equation; from this estimate, we derive a Lyapunov asymptotic stability test for this equation. Here the results by Faedo and Kharitonov on the Hurwitz conditions for families of polynomials find a natural application. Similar statements are obtained for a system of linear differential equations.
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Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu · Mathematica Bohemica · 2004
We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.
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Lars Grüne, Eduardo D. Sontag, Fabian R. Wirth · 1999
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Nah-Oak Song, B.-J. Kwak, Leonard E. Miller · Journal of Research of the National Institute of Standards and Technology · 2003
Random access schemes for packet networks featuring distributed control require algorithms and protocols for resolving packet collisions that occur as the uncoordinated terminals contend for the channel. A widely used collision resolution protocol is the exponential backoff (EB). New analytical results for the stability of the (binary) EB are given. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were used. In this paper, care is taken to use a model that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. We show that r = 1/(1 - e(-1)) is the optimum backoff factor that maximizes the throughput. The accuracy of the analysis is checked against simulation results.
Cited by 47Open access