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SUMMARY:Christoph Kawan (LMU München\, Germany)
DTSTART;VALUE=DATE-TIME:20210708T150000Z
DTEND;VALUE=DATE-TIME:20210708T160000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130300Z
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:20210926T130300Z
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:20210926T130300Z
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:20210926T130300Z
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:Ricardo Sanfelice (UC Santa Cruz\, USA)
DTSTART;VALUE=DATE-TIME:20211021T150000Z
DTEND;VALUE=DATE-TIME:20211021T160000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130300Z
UID:ISS-Theory/5
DESCRIPTION:by Ricardo Sanfelice (UC Santa Cruz\, USA) as part of Input-to
-State Stability and its Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/5/
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:20210926T130300Z
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:20210926T130300Z
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:20210926T130300Z
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:Felix Schwenninger (TU Twente\, the Netherlands)
DTSTART;VALUE=DATE-TIME:20211014T150000Z
DTEND;VALUE=DATE-TIME:20211014T160000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130300Z
UID:ISS-Theory/9
DESCRIPTION:by Felix Schwenninger (TU Twente\, the Netherlands) as part of
Input-to-State Stability and its Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rami Katz (Tel-Aviv University)
DTSTART;VALUE=DATE-TIME:20211209T160000Z
DTEND;VALUE=DATE-TIME:20211209T170000Z
DTSTAMP;VALUE=DATE-TIME:20210926T130300Z
UID:ISS-Theory/10
DESCRIPTION:by Rami Katz (Tel-Aviv University) as part of Input-to-State S
tability and its Applications\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ISS-Theory/10/
END:VEVENT
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