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Convergence Properties for Discrete-time Nonlinear Systems [article]

Duc N. Tran, Björn S. Rüffer, Christopher M. Kellett
<span title="2018-11-04">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we investigate the differences between these convergence properties for discrete-time, time-varying nonlinear systems by comparing the properties in pairs and using examples.  ...  Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis.  ...  Finally, we provide a discrete-time Demidovič condition that is sufficient for all three properties. 4.1. Incremental Stability vs. Convergent Dynamics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1612.05327v3">arXiv:1612.05327v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/enoohgfnhfckvks4xe5dm2ohne">fatcat:enoohgfnhfckvks4xe5dm2ohne</a> </span>
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Definitions of incremental stability for hybrid systems

R. Postoyan, J.J.B. Biemond, W.P.M.H. Heemels, N. van de Wouw
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2015 54th IEEE Conference on Decision and Control (CDC)</a> </i> &nbsp;
We present definitions for incremental stability depending on whether incremental asymptotic stability properties hold with respect to the hybrid time, the continuous time, or the discrete time, respectively  ...  The definitions are shown to be consistent with those available in the literature for continuous-time and discrete-time systems. R. Postoyan is with the  ...  Additionally, we define the symmetric notion of jump uniform (pre-)incremental asymptotic stability for hybrid systems which exhibit incremental stability properties with respect to the discrete time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2015.7403088">doi:10.1109/cdc.2015.7403088</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/PostoyanBHW15.html">dblp:conf/cdc/PostoyanBHW15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yobbhd2ysfajpjtvpiglqsjoee">fatcat:yobbhd2ysfajpjtvpiglqsjoee</a> </span>
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A contractivity approach for probabilistic bisimulations of diffusion processes

Alessandro Abate
<span title="">2009</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference</a> </i> &nbsp;
This relationship leads to a procedure that constructs a discrete approximation of a diffusion process. The procedure is based on the discretization of space and time.  ...  Furthermore, we show that the notion of stochastic contractivity is related to a probabilistic version of the concept of incremental stability.  ...  PROBABILISTIC INCREMENTAL STABILITY Contractivity is a property that can be used to study certain stability properties of a system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2009.5400334">doi:10.1109/cdc.2009.5400334</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/Abate09.html">dblp:conf/cdc/Abate09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/amg47n4q4zhvrcvqfdksp627zi">fatcat:amg47n4q4zhvrcvqfdksp627zi</a> </span>
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Networked Embedded Control Systems: from Modelling to Implementation

Maria Domenica Di Benedetto, Giordano Pola
<span title="2013-08-22">2013</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
Networked Embedded Control Systems are distributed control systems where the communication among plants, sensors, actuators and controllers occurs in a shared network.  ...  We first generalized the notion of incremental input-to-state stability from nonlinear control systems to nonlinear time-delay systems and provide sufficient conditions for checking this property in terms  ...  Recent results include work on controllable discrete-time linear systems [28] , piecewise-affine and multi-affine systems [14, 4] , set-oriented discretization for discrete-time nonlinear optimal control  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.124.3">doi:10.4204/eptcs.124.3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/svibbbn23bag7m4ol5q7rcjrbu">fatcat:svibbbn23bag7m4ol5q7rcjrbu</a> </span>
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A Framework for Robust Stability of Systems Over Finite Alphabets

Danielle C. Tarraf, Alexandre Megretski, Munther A. Dahleh
<span title="">2008</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tiaci7xy45hczhz755zlpu5h7q" style="color: black;">IEEE Transactions on Automatic Control</a> </i> &nbsp;
Systems over finite alphabets are discrete-time systems whose input and output signals take their values in finite sets.  ...  Finally, incremental stability and external stability are shown to be equivalent notions for this class of systems.  ...  The authors would like to thank the Associate Editor and the anonymous reviewers for valuable feedback and suggestions for improving the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tac.2008.923658">doi:10.1109/tac.2008.923658</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ttj3zhotqzc6pjcgwpa3i6aufe">fatcat:ttj3zhotqzc6pjcgwpa3i6aufe</a> </span>
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Page 753 of Mathematical Reviews Vol. , Issue 2003A [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The paper presents necessary and sufficient conditions for incremental stability in terms of the existence of Lyapunov functions.  ...  To characterize input-output relations with respect to the incremental stability the notion of incremental input- to-state stability is introduced.  ... 
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Page 529 of Mathematical Reviews Vol. , Issue 93a [page]

<span title="">1993</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this paper, we establish the equivalence of various second moment stability properties (mean square stability, stochastic stability and exponential mean square stability) for discrete-time Markovian  ...  A. (1-CWR-E) Stability and control of discrete-time jump linear systems. Control Theory Adv. Tech. 7 (1991), no. 2, 247-270.  ... 
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On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems

M. De la Sen
<span title="">2017</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3s4wom7forhp3klujcroiocrpi" style="color: black;">Discrete Dynamics in Nature and Society</a> </i> &nbsp;
Such properties are very relevant in stability theory since they refer to global stability properties of passive feed-forward, in general, nonlinear, and time-varying controlled systems controlled via  ...  Some of the obtained results are also directly related to input-passivity, output-passivity, and hyperstability properties in controlled dynamic systems.  ...  Acknowledgments The author is very grateful to the Spanish Government and European Fund of Regional Development FEDER for Grant DPI2015-64766-R and to UPV/EHU for Grant PGC 17/33.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2017/1497867">doi:10.1155/2017/1497867</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v6b5aahxhbditijyoypjywrfc4">fatcat:v6b5aahxhbditijyoypjywrfc4</a> </span>
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Book Announcements [Bookshelf]

<span title="">2018</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ur4yxqfrung6xlhkqhxxghyovy" style="color: black;">IEEE Control Systems</a> </i> &nbsp;
This brief covers stoc hast ic control by highlighting recent advances in the design of optimal controllers for Markov jump linear systems.  ...  It also presents an algorithm that attempts to solve this open stochastic control problem and provides a real-time application for controlling the speed of direct current motors.  ...  It treats linear systems in state-space form in both continuous and discrete time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/mcs.2018.2810560">doi:10.1109/mcs.2018.2810560</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e33m4aegibhq5kz3kvmz2mfbmm">fatcat:e33m4aegibhq5kz3kvmz2mfbmm</a> </span>
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Scanning the Issue

<span title="">2018</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tiaci7xy45hczhz755zlpu5h7q" style="color: black;">IEEE Transactions on Automatic Control</a> </i> &nbsp;
The paper presents the characterizations of global asymptotic stability, input-to-state stability, and incremental input-to-state stability for discrete-time nonlinear systems with uncertain and time-varying  ...  Necessary and sufficient conditions for global asymptotic stability and for input-to-state stability, and sufficient conditions for incremental input-to-state stability, in terms of discrete-time Lyapunov-Krasovskii  ...  Domenica Di Benedetto The paper presents the characterizations of global asymptotic stability, input-to-state stability, and incremental input-to-state stability for discrete-time nonlinear systems with  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tac.2018.2826728">doi:10.1109/tac.2018.2826728</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vheehtx7rre75oancfobi3y7qm">fatcat:vheehtx7rre75oancfobi3y7qm</a> </span>
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Contraction Analysis and Control Synthesis for Discrete-time Nonlinear Processes [article]

Lai Wei, Ryan McCloy, Jie Bao
<span title="2022-05-09">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The discrete-time differential dissipativity condition is further developed, which can be used for control designs for disturbance rejection.  ...  This article presents a systematic approach to the implementation of contraction-based control for discrete-time nonlinear processes.  ...  an explicit proof for exponential incremental convergence analysis of contracting discrete-time nonlinear systems, and a controller structure for discrete-time contraction is developed (as an extension  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.04699v2">arXiv:2112.04699v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ncun3a6jsfgnjgdmxac4xf7tn4">fatcat:ncun3a6jsfgnjgdmxac4xf7tn4</a> </span>
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Page 6669 of Mathematical Reviews Vol. , Issue 2004h [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(F-CAEN-API; Caen) The behavior of incrementally stable discrete time systems. (English summary) Systems Control Lett. 46 (2002), no. 4, 289-301.  ...  The paper aims at the derivation of model-based control laws that attain the invariance objective for nonlinear skew-product discrete-time systems.  ... 
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Input/output stability of systems over finite alphabets

D. Tarraf, A. Megretski, M.A. Dahleh
<span title="">2006</span> <i title="IEEE"> 2006 American Control Conference </i> &nbsp;
This paper considers systems over finite alphabets, that is discrete-time systems whose input and output signals take their values in finite sets.  ...  Sufficient conditions for stability of feedback interconnections of stable systems, in the finite gain and incremental sense, are derived.  ...  SYSTEMS AND STABILITY A. Systems over Finite Alphabets We begin by defining a discrete-time system over finite alphabets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/acc.2006.1657351">doi:10.1109/acc.2006.1657351</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/paft7jmrgvahjanr4k4ugklb4y">fatcat:paft7jmrgvahjanr4k4ugklb4y</a> </span>
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Incremental Stability of Hybrid Dynamical Systems

J. J. Benjamin Biemond, Romain Postoyan, W.P.M.H. Heemels, Nathan Van De Wouw
<span title="">2018</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tiaci7xy45hczhz755zlpu5h7q" style="color: black;">IEEE Transactions on Automatic Control</a> </i> &nbsp;
To present Lyapunov conditions for these two notions, in both cases, we resort to an extended hybrid system and we prove that the stability of a well-defined set for this extended system implies incremental  ...  To overcome this issue, we present novel definitions of incremental stability for hybrid systems based on graphical closeness of solutions.  ...  Consistent with incremental stability definitions for continuous-time in [1] and discrete-time systems in [25] , we define incremental stability as a uniform asymptotic stability property.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tac.2018.2830506">doi:10.1109/tac.2018.2830506</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2lwmw2c3hrdfvllzx4pfkvexam">fatcat:2lwmw2c3hrdfvllzx4pfkvexam</a> </span>
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Discrete and continuous fractional persistence problems – the positivity property and applications

Jacky Cresson, Anna Szafrańska
<span title="">2017</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k7mu2abycrg6znsheqexp2qnwm" style="color: black;">Communications in nonlinear science &amp; numerical simulation</a> </i> &nbsp;
unconditionally on the discretization increment.  ...  In this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case  ...  Positivity property : A fractional differential system of the form (7) satisfies the positivity property is for all initial conditions x 0 ∈ R m + , the solution φ t (x 0 ) passing through x 0 at time  ... 
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