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BEGIN:VEVENT
SUMMARY:Christoph Kawan (LMU München\, Germany)
DTSTART;VALUE=DATE-TIME:20210708T150000Z
DTEND;VALUE=DATE-TIME:20210708T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/1
DESCRIPTION:Title: A Lyapunov-based small-gain approach to ISS of infinite nonlinear netwo
rks\nby Christoph Kawan (LMU München\, Germany) as part of Input-to-S
tate Stability and its Applications\n\n\nAbstract\nIn this talk\, I presen
t an approach to the verification of\ninput-to-state stability for network
ed control systems composed of a\ncountably infinite number of nonlinear s
ubsystems. The essential\nrequirements on these subsystems are that they a
re finite-dimensional\,\ncontinuous in time and each of them is influenced
only by finitely many\nother subsystems. Assuming that each subsystem adm
its an ISS Lyapunov\nfunction with respect to both internal inputs (influe
nces from other\nsubsystems) and external inputs (control inputs)\, our re
sult provides\nsufficient conditions for the existence of an ISS Lyapunov
function for\nthe whole network. This Lyapunov function is built from the
Lyapunov\nfunctions of the subsystems and it is important to note that the
ISS\nestimates for the later are given in the max-type formulation. This\
nformulation allows for the definition of an associated max-type gain\nope
rator Gamma\, encoding the influence of the\nsubsystems on each other via
nonlinear gain functions. The operator\nGamma acts as a monotone operator
on the positive cone of \\ell_{\\infty}.\nThe essential requirement on Gam
ma is that it admits a so-called path of\nstrict decay\, a condition which
is known to be equivalent to the\nclassical small-gain condition in the c
ase of finite networks. For\ninfinite networks\, however\, this equivalenc
e does not hold. Still\, as in\nfinite dimensions\, the existence of a pat
h of strict decay is linked to\nthe stability properties of the discrete-t
ime system generated by the\ngain operator. In my talk\, I will try to\nex
plain the difficulties involved with the stability analysis of this\nsyste
m.\n\nJoint work with Andrii Mironchenko and Majid Zamani\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iasson Karafyllis (National Technical University of Athens\, Greec
e)
DTSTART;VALUE=DATE-TIME:20210715T150000Z
DTEND;VALUE=DATE-TIME:20210715T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/2
DESCRIPTION:Title: IOS-gains and asymptotic gains for linear systems\nby Iasson Karafy
llis (National Technical University of Athens\, Greece) as part of Input-t
o-State Stability and its Applications\n\n\nAbstract\nThe talk will be dev
oted to the presentation of a fundamental relation between Output \nAsympt
otic Gains (OAG) and Input-to-Output Stability (IOS) gains for li
near \nsystems. More specifically\, it will be shown that for eve
ry Input-to-State Stable\, \nstrictly causal linear system the minimum O
AG is equal to the minimum IOS-gain. \nMoreover\, both quantities can
be computed by solving a specific optimal control \nproblem and by
considering periodic inputs only. The result is valid for wide classes \no
f linear systems (including delay systems or systems described by
PDEs). The \ncharacterization of the minimum IOS-gain is importan
t because it allows the non-\nconservative computation of the IOS
-gains\, which can be used in a small-gain \nanalysis. A number
of cases of finite-dimensional linear systems will also be \nprese
nted\, where exact computation of the minimum IOS-gain can be pe
rformed. \nLinks to notions used extensively in the literature of linear s
ystems (e.g.\, the BIBO \nnorm or the notion of an admissible operator) wi
ll be provided.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miroslav Krstic (UC San Diego\, USA)
DTSTART;VALUE=DATE-TIME:20210722T150000Z
DTEND;VALUE=DATE-TIME:20210722T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/3
DESCRIPTION:Title: Fixed-Time ISS and Prescribed-Time Stabilization\nby Miroslav Krsti
c (UC San Diego\, USA) as part of Input-to-State Stability and its Applica
tions\n\n\nAbstract\nIn prescribed-time stabilization the task is to desig
n a feedback law that guarantees completion of the convergence to a set po
int no later than a time that is prescribed by the user and independent of
the initial condition of the plant. When the plant model is known perfect
ly and the full state is measured\, ISS issues do not arise. However\, in
the presence of disturbances or under observer-based feedback\, ISS with r
espect to various inputs becomes of interest. Perhaps unexpectedly\, once
prescribed-time stabilization is achieved\, an ISS-like property stronger
than the conventional ISS is obtained as a bonus. Specifically\, the origi
n\, which is not necessarily the system’s equilibrium\, is made attracti
ve in prescribed time even in the presence of non-vanishing disturbances.
Or\, in simpler language\, the ISS gain is a function of time and decays t
o zero at the terminal time. I will discuss the ISS issues associated with
prescribed-time feedback design for general linear ODEs\, some nonlinear
ODEs with a disturbance matched by control\, and briefly for parabolic PDE
s (in hyperbolic PDEs\, finite-time stabilization\, when possible\, is obt
ained as easily as exponential stabilization).\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Postoyan (CNRS\, Université de Lorraine\, France)
DTSTART;VALUE=DATE-TIME:20210729T150000Z
DTEND;VALUE=DATE-TIME:20210729T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/4
DESCRIPTION:Title: Event-Triggered Control Through the Eyes of Hybrid Small-Gain Theorem\nby Romain Postoyan (CNRS\, Université de Lorraine\, France) as part o
f Input-to-State Stability and its Applications\n\n\nAbstract\nA common ap
proach to design event-triggered controllers is emulation. The idea is to
first construct a feedback law in continuous-time\, which ensures the desi
red closed-loop properties. Then\, the communication constraints between t
he plant and the controller are taken into account and a triggering rule i
s synthesized to generate the transmission instants in such a way that the
properties of the continuous-time closed-loop system are preserved\, and
a strictly positive minimum inter-event time exists\, which is essential i
n practice.\n\nVarious triggering rules have been proposed in this context
in the literature\, including relative threshold\, fixed threshold\, dyna
mic triggering law to mention a few. We will show in this talk that these
seemingly unrelated techniques can all be interpreted in a unified manner.
Indeed\, it appears that all them guarantee the satisfaction of the condi
tions of a hybrid small-gain theorem. This unifying perspective provides c
lear viewpoints on the essential differences and similarities of existing
event-triggering policies. Interestingly\, for all the considered laws\, t
he small-gain condition vacuously holds in the sense that one of the inter
connection gains is zero. We then exploit this fact to modify the original
triggering law in such a way that the small-gain condition is no longer t
rivially satisfied. By doing so\, we obtain redesigned strategies\, which
may reduce the number of transmissions as illustrated by an example.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Polyakov (Inria Lille Nord-Europe / CNRS CRIStAL)
DTSTART;VALUE=DATE-TIME:20211007T150000Z
DTEND;VALUE=DATE-TIME:20211007T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/6
DESCRIPTION:Title: On Input-to-State Stability of Homogeneous Evolution Equations\nby
Andrey Polyakov (Inria Lille Nord-Europe / CNRS CRIStAL) as part of Input-
to-State Stability and its Applications\n\n\nAbstract\nHomogeneity is a sy
mmetry of an object with respect to a dilatation. All linear and many\nnon
linear models of mathematical physics are homogeneous. For example\, Burge
rs\, KdV and Navier-Stokes \nequations are symmetric with respect to a pro
perly selected dilation. Finite dimensional homogeneous control\nsystems
are known to be similar with linear ones\, but they may have a better reg
ulation quality like\na faster convergence\, stronger robustness and less
overshoot. This talk is devoted to Input-to-State Stability analysis\nof
homogeneous evolution equations in Banach spaces. Similarly to the finite-
time dimensional case\, it is shown that\nthe uniform asymptotic stability
of homogeneous unperturbed system guarantees its Input-to-State Stability
\nwith respect to homogeneously involved perturbations.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine Chaillet (L2S - CentraleSupélec - Univ. Paris Saclay)
DTSTART;VALUE=DATE-TIME:20211028T150000Z
DTEND;VALUE=DATE-TIME:20211028T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/7
DESCRIPTION:Title: Point-wise dissipation in time-delay systems: recent results and open q
uestions\nby Antoine Chaillet (L2S - CentraleSupélec - Univ. Paris Sa
clay) as part of Input-to-State Stability and its Applications\n\n\nAbstra
ct\nIn the existing characterizations of input-to-state stability (ISS) fo
r time-delay systems\, the Lyapunov-Krasovskii functional (LKF) has a $\\m
athcal K_\\infty$ dissipation rate that involves the whole LKF itself (LKF
-wise dissipation) or even the supremum norm of the state history (history
-wise dissipation). A similar characterization holds for integral input-to
-state stability (iISS)\, in which the dissipation rate is just a positive
definite function. These characterizations have allowed to extend several
results on ISS and iISS from finite dimension to time-delay systems.\n\nN
evertheless\, in practice\, obtaining a LKF-wise or history-wise dissipati
on is not always an easy task and often resorts to rather artificial trick
s. More crucially\, in the absence of inputs\, it is known from the work o
f N. Krasovskii that a dissipation involving merely the current value of t
he state norm (point-wise dissipation) is enough to guarantee global asymp
totic stability.\n\nIn this talk\, we investigate whether a point-wise dis
sipation suffices to conclude ISS or iISS for time-delay systems. We give
a positive answer to this question for iISS. More precisely\, we show that
point-wise\, LKF-wise and history-wise dissipations through a positive de
finite function all ensure iISS. \n\nFor ISS\, despite strong efforts\, th
is question remains open: it has not yet be proved or disproved that ISS i
s equivalent to the existence of a point-wise dissipation. We identify two
classes of systems for which this is the case\, by imposing a growth rest
riction either on the upper bound of the LKF or on the vector field. We al
so provide some insights on what can be said about a system having a point
-wise dissipation to hopefully foster some creative discussion.\n\nFinally
\, while asymptotic stability is known for long to be equivalent to a poin
t-wise dissipation for input-free systems\, this question remains open for
exponential stability. We show that\, at least for systems ruled by a glo
bally Lipschitz vector field\, global exponential stability is guaranteed
under a point-wise dissipation.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Seminar this week\, but consider taking part in the SCINDIS Wo
rkshop (27-29 Sep 2021\, fully online\, zero conference fee)
DTSTART;VALUE=DATE-TIME:20210930T150000Z
DTEND;VALUE=DATE-TIME:20210930T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/8
DESCRIPTION:Title: 3rd Workshop on Stability and Control of Infinite-Dimensional Systems (
SCINDIS 2020)\nby No Seminar this week\, but consider taking part in t
he SCINDIS Workshop (27-29 Sep 2021\, fully online\, zero conference fee)
as part of Input-to-State Stability and its Applications\n\n\nAbstract\nV
isit the homepage of SCINDIS:\nhttps://www.fan.uni-wuppertal.de/de/scindis
-2020.html\n\nThe scope of the Workshop includes but is not limited to\n
\n >Stability and control of partial differential equations\n >Stability
and control of time-delay systems\n >Input-to-state stability of infinit
e-dimensional systems\n >Stabilizability of infinite-dimensional systems\
n >Semigroup and admissibility theory\n\nOrganizers:\nSergey Dashkovskiy\
nBirgit Jacob \nAndrii Mironchenko\nFabian Wirth\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rami Katz (Tel-Aviv University\, Israel)
DTSTART;VALUE=DATE-TIME:20211209T160000Z
DTEND;VALUE=DATE-TIME:20211209T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/10
DESCRIPTION:Title: Finite-dimensional observer-based ISS and $L^2$-gain control of parabo
lic PDEs\nby Rami Katz (Tel-Aviv University\, Israel) as part of Input
-to-State Stability and its Applications\n\n\nAbstract\nFinite-dimensional
observer-based controller design for PDEs is a challenging problem. In th
is talk\, construction of such controllers via the modal decomposition met
hod for linear parabolic 1D PDEs will be presented. We will start with fin
ite-dimensional observer-based control for the linear heat equation where
at least one of the control or observation operators is bounded. We will p
roceed with the case of both operators unbounded\, where dynamic extension
is helpful. Here we will consider ISS and $L^2$-gain analysis of the Kura
moto-Sivashinsky equation. The extension of the results to time-varying in
put/output delays\, as well as arbitrarily large constant input delays wil
l be presented. Finally\, we will discuss sampled-data implementation of
ﬁnite-dimensional boundary controllers for the 1D heat equation under di
screte-time point measurement\, via a generalized hold device. An essentia
l tool for the ISS analysis will be a novel ISS Halanay’s inequality wit
h explicit constants in the bounds.\n\nJoint work with Prof. Emilia Fridma
n\nhttps://scholar.google.co.il/citations?user=szPJQlkAAAAJ&hl=en\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Schwenninger (TU Twente\, the Netherlands)
DTSTART;VALUE=DATE-TIME:20211202T160000Z
DTEND;VALUE=DATE-TIME:20211202T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/11
DESCRIPTION:Title: Recent results on ISS Lyapunov functions\nby Felix Schwenninger (T
U Twente\, the Netherlands) as part of Input-to-State Stability and its Ap
plications\n\n\nAbstract\nLike in many branches of dynamical systems\, Lya
punov functions play a pivotal role in the study of input-to-state stabili
ty.\nIn this talk we discuss recent investigations around such coercive an
d non-coercive Lyapunov functions in the context of infinite-dimensional s
ystems. A focus is laid on general linear PDEs subject to boundary control
.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Sanfelice (University of California\, Santa Cruz\, USA)
DTSTART;VALUE=DATE-TIME:20211118T160000Z
DTEND;VALUE=DATE-TIME:20211118T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/12
DESCRIPTION:Title: Observers for Hybrid Dynamical Systems: Models\, Necessary Conditions\
, and Systematic Design\nby Ricardo Sanfelice (University of Californi
a\, Santa Cruz\, USA) as part of Input-to-State Stability and its Applicat
ions\n\n\nAbstract\nIn most control applications\, estimating the state of
a system is crucial\, whether it be for control\, supervision\, or fault
diagnosis purposes. Unfortunately\, the problem of designing observers for
systems with state variables that evolve continuously\, and at times\, ju
mp -- namely\, hybrid systems -- in a general setting is unsolved. One of
the main challenges in the design of observers for such systems is the fa
ct that hybrid behavior may lead to system trajectories from nearby initia
l conditions that have different jump times. Such a mismatch of jump times
makes the formulation of observability/detectability and\, in turn\, obse
rver design very challenging. After a brief introduction to hybrid dynami
cal systems\, recent advancements towards the systematic design of observe
rs for hybrid systems will be presented. Specifically\, a general framew
ork for state estimation of plants modeled as hybrid dynamical systems\, b
oth in the favorable case where the jumps of the plant and of the observer
occur at the same time and when they occur at different (but nearby) time
s\, will be introduced. With a suitable notion of observer for hybrid dyn
amical systems and relying on reparameterizations of the hybrid signals in
volved\, it will be shown that an appropriate detectability notion is nece
ssary for the existence of an observer\, or better said\, a hybrid observe
r. Applications and examples will be presented to illustrate the concepts
and results. This research is joint work with Professor Pauline Bernard
at MINES ParisTech (https://sites.google.com/site/sitepmbernard/home).\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aneel Tanwani (LAAS-CNRS\, Toulouse\, France)
DTSTART;VALUE=DATE-TIME:20220113T160000Z
DTEND;VALUE=DATE-TIME:20220113T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/13
DESCRIPTION:Title: Input-to-State Stability of Switched Systems under Dwell-Time Conditio
ns\nby Aneel Tanwani (LAAS-CNRS\, Toulouse\, France) as part of Input-
to-State Stability and its Applications\n\n\nAbstract\nAbstract: Stability
analysis of switched systems has been a topic of interest for more than t
wo decades\, and the conditions based on dwell-time notions form an import
ant part of this literature. In particular\, input-to-state stability (ISS
) and different variants of ISS have also been studied using similar dwell
-time conditions on the switching signals. Earlier approaches in this dire
ction\, based on multiple Lyapunov functions\, typically require exponenti
ally decaying Lyapunov functions which are compatible with other subsystem
s. However\, such compatibility may not hold for switched nonlinear system
s in general\, where the individual Lyapunov functions admit nonlinear sup
ply functions. In this talk\, I will start with a quick overview of earlie
r results on ISS using dwell-time conditions. Then\, I will provide some e
xamples of switched nonlinear systems which are not ISS for arbitrarily la
rge values of dwell-time\, even though individual subsystems are ISS. Neve
rtheless\, under certain conditions on Lyapunov functions (which admit non
linear supply functions)\, we can derive new dwell-time bounds\, which gua
rantee ISS of switched systems. We will see the utility of such conditions
in analyzing stability of cascade interconnections of switched systems an
d an application in sampled-data control using dynamic output feedback.\n\
nReferences:\n[1] M. Della Rossa and A. Tanwani. Instability of Dwell-Time
Constrained Switched Nonlinear Systems. Under review in Systems & Control
Letters\, June 2021. Preprint available on request.\n[2] S. Liu\, A. Tanw
ani and D. Liberzon. ISS and Integral ISS of Switched Systems with Nonline
ar Supply Functions. Mathematics of Controls\, Signals\, and Systems\, 202
1. DOI: 10.1007/s00498-021-00306-x\n[3] G.X. Zhang and A. Tanwani. ISS Lya
punov Functions for Cascade Switched Systems and Sampled-Data Control\, Au
tomatica\, 105: 216—227\, 2019.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierdomenico Pepe (University of L'Aquila)
DTSTART;VALUE=DATE-TIME:20220120T160000Z
DTEND;VALUE=DATE-TIME:20220120T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/14
DESCRIPTION:Title: Nonlinear Halanay's Inequalities for ISS of Retarded Systems: the Cont
inuous and the Discrete Time Case\nby Pierdomenico Pepe (University of
L'Aquila) as part of Input-to-State Stability and its Applications\n\n\nA
bstract\nNonlinear versions of continuous-time and discrete-time Halanay's
inequalities are presented as sufficient conditions for the convergence o
f involved functions to the origin\, uniformly with respect to bounded set
s of initial values. The same results are shown in the case forcing terms
are also present\, for the uniform convergence to suitable neighborhoods o
f the origin. Related Lyapunov methods for the global uniform asymptotic s
tability and the input-to-state stability of systems described by retarded
functional differential equations and by discrete-time equations with del
ays are shown. \n\nReferences:\n[1] Pierdomenico Pepe\, A Nonlinear Versio
n of Halanay’s Inequality for the Uniform Convergence to the Origin\, Ma
thematical Control and Related Fields\, 2021\, doi: 10.3934/mcrf.2021045
\n\n[2] Maria Teresa Grifa\, Pierdomenico Pepe\, On Stability Analysis of
Discrete-Time Systems With Constrained Time-Delays via Nonlinear Halanay-T
ype Inequality\, IEEE Control Systems Letters\, Volume 5\, Issue 3\, July
2021\, doi: 10.1109/LCSYS.2020.3007096\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilfrid Perruquetti (Ecole Centrale de Lille\, CNRS\, France)
DTSTART;VALUE=DATE-TIME:20220203T160000Z
DTEND;VALUE=DATE-TIME:20220203T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/15
DESCRIPTION:Title: Non-Asymptotic output feedback of a double integrator: a separation pr
inciple.\nby Wilfrid Perruquetti (Ecole Centrale de Lille\, CNRS\, Fra
nce) as part of Input-to-State Stability and its Applications\n\n\nAbstrac
t\nUsually\, in control/estimation problems\, one is looking at exponentia
l decaying rates for many reasons: ease of understanding\, many tools for
tuning and getting a time response estimate. But nowadays\, control theory
has to meet more and more demanding performances in many areas such as ae
rospace\, manufacturing\, robotics and transportation to mention a few. A
necessary property for these algorithms is stability. The convergence time
for the system to reach the goal may be infinite (e.g.\, asymptotic or ex
ponential convergence) or finite. Combining stability with these convergen
ce types leads to asymptotic or non-asymptotic stability properties. \n\nT
hese concepts may help in obtaining a separation principle when designing
output feedback as seen on an example for an double integrator system wher
e ISS properties of homogeneous systems is applied without building a Lyap
unov function for the closed-loop system.\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Guiver (Edinburgh Napier University)
DTSTART;VALUE=DATE-TIME:20220210T160000Z
DTEND;VALUE=DATE-TIME:20220210T170000Z
DTSTAMP;VALUE=DATE-TIME:20221209T230628Z
UID:ISS-Theory/16
DESCRIPTION:Title: The exponential input-to-state stability property — characterisation
s and feedback interconnections\nby Chris Guiver (Edinburgh Napier Uni
versity) as part of Input-to-State Stability and its Applications\n\n\nAbs
tract\nThe exponential input-to-state stability (ISS) property is consider
ed for systems of controlled nonlinear differential equations\, and a char
acterisation in terms of an exponential ISS Lyapunov function is establish
ed. A natural concept of linear state/input-to-state L2-gain is\nintroduce
d\, and the equivalence of this property and exponential ISS is establishe
d. Further\, the feedback interconnection of two exponentially ISS systems
is shown to be exponentially ISS provided a suitable small-gain condition
is satisfied.\n\nJoint work with Hartmut Logemann\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/16/
END:VEVENT
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