A Small-Gain Condition for Interconnections of ISS Systems With Mixed ISS Characterizations

Dashkovskiy, Sergey; Kosmykov, Michael; Wirth, Fabian

doi:10.1109/tac.2010.2080110

Cited by 40 publications

(9 citation statements)

References 23 publications

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“…Introduce stopping times σ k and σ ∞ as in (10) and (11). By Lemma 1, the local Lipschitz condition and local boundedness of f and g, and the adaption and measurability of u guarantee the existence of the unique solution x(t) to system (23) on [t 0 , σ ∞ ).…”

Section: Dissipativity Of Stochastic Network Systemsmentioning

confidence: 99%

Small-gain conditions for stochastic network systems

Karimi

Shi

2013

52nd IEEE Conference on Decision and Control

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In this paper, some small-gain conditions are presented for stochastic network systems which can describe many large-scale systems with interconnections, nonlinear behaviors, uncertainties and random disturbances. One subsystem is selected as monitor with the requirement that the gains to other systems are smooth concave functions. The relations of members under the supervise of the monitor are described as bilateral plus multilateral relations of gains. For the deterministic case, the requirement on the monitor can be removed. To demonstrate the power of this result, the small-gain conditions cover interconnected system with two subsystems as a special case. Compared with the existing results, the main character is that the forward completion of system and ultimate uniform boundedness of input are removed from conditions of smallgain theorems.

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Section: Dissipativity Of Stochastic Network Systemsmentioning

confidence: 99%

Small-gain conditions for stochastic network systems

Karimi

Shi

2013

52nd IEEE Conference on Decision and Control

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“…Many advances in the ISS theory were made in the following decades, for example, establishing the sufficient and necessary conditions to characterize a system as ISS . Also, the interconnection of systems has been a central subject in many works, resulting in some useful and widely known theorems such as a Lyapunov‐based nonlinear small gain theorem , or a small gain theorem for systems with mixed ISS characterizations . On the other hand, many Lyapunov approaches have been developed to facilitate the ISS analysis by means of Lyapunov functions .…”

Section: Introductionmentioning

confidence: 99%

Output feedback sliding‐mode control with unmatched disturbances, an ISS approach

Aparicio

Castaños

2016

Intl J Robust & Nonlinear

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The robustness properties of a first-order sliding-mode controller are combined with those of an added linear term in order to obtain a closed loop that shows input-to-state stability with respect to matched and unmatched disturbances, of which an upper bound might not be known, using only output information. The output under consideration can have any relative degree. Also, a transformation of the state into a novel output normal form is presented. The zero dynamics are considered unstable and perturbed, so a methodology for defining an observer and a virtual control for it is presented.

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“…Focusing on Internet-based teleoperation based on delay-dependent control schemes which can provide better transparency properties, the real problem is to establish delay-dependent conditions for systems with two internal control loops (master and slave) ”connected” by (time-varying) delayed signals. This problem can be solved—to name just two possible approaches—by applying delay-dependent stability tools developed for time-domain techniques that are based on Lyapunov-Krasovskii functionals, with a formulation of stability obtained via easily computable LMI conditions (see [ 6 , 10 , 19 , 20 ] and references therein), or by using approaches based on small-gain type theorems in the input-to-state stability framework [ 21 ], which can be used even when passivity is lost.…”

Section: Introductionmentioning

confidence: 99%

Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays

Delgado

Barreiro

Falcon

et al. 2016

Sensors

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We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency.

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A Small-Gain Condition for Interconnections of ISS Systems With Mixed ISS Characterizations

Cited by 40 publications

References 23 publications

Small-gain conditions for stochastic network systems

Small-gain conditions for stochastic network systems

Output feedback sliding‐mode control with unmatched disturbances, an ISS approach

Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays

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