A Multichannel IOS Small Gain Theorem for Systems With Multiple Time-Varying Communication Delays

Polushin, Ilia G.; Marquez, Horacio J.; Tayebi, Abdelhamid; Liu, Peter

doi:10.1109/tac.2008.2009582

Cited by 60 publications

(52 citation statements)

References 16 publications

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“…For continuous-time systems a similar relation was also observed in [23,25,29] and in the context of integral ISS in [8,9]. However, the derivations for continuous-time systems rely on different arguments.…”

Section: Remarksupporting

confidence: 61%

Input-to-state stability analysis for interconnected difference equations with delay

Gielen

Lazăr

Teel

2012

Math. Control Signals Syst.

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Input-to-state stability (ISS) of interconnected systems with each subsystem described by a difference equation subject to an external disturbance is considered. Furthermore, special attention is given to time delay, which gives rise to two relevant problems: (i) ISS of interconnected systems with interconnection delays, which arise in the paths connecting the subsystems, and (ii) ISS of interconnected systems with local delays, which arise in the dynamics of the subsystems. The fact that a difference equation with delay is equivalent to an interconnected system without delay is the crux of the proposed framework. Based on this fact and small-gain arguments, it is demonstrated that interconnection delays do not affect the stability of an interconnected system if a delay-independent small-gain condition holds. Furthermore, also using small-gain arguments, ISS for interconnected systems with local delays is established via the Razumikhin method as well as the Krasovskii approach. A combination of the results for interconnected systems with interconnection delays and local delays, respectively, provides a framework for ISS analysis of general interconnected systems with delay. Thus, a scalable ISS analysis method is obtained for large-scale interconnections of difference equations with delay.

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Section: Remarksupporting

confidence: 61%

Input-to-state stability analysis for interconnected difference equations with delay

Gielen

Lazăr

Teel

2012

Math. Control Signals Syst.

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“…and F * PIL (t) refer to the exogenous forces applied by the therapist and the patient, which belong to the L ∞ space [12], while F † T (t), F † PFL (t) and F † PIL (t) indicate the outputs of the systems Ξ 4 (s), Ξ 5 (s) and Ξ 6 (s) for inputs F * T (t), F * PFL (t) and…”

Section: Closed-loop Stability Analysismentioning

confidence: 99%

Therapist-in-the-Loop robotics-assisted mirror rehabilitation therapy: An Assist-as-Needed framework

Shahbazi

Atashzar

Tavakoli

et al. 2015

2015 IEEE International Conference on Robotics and Automation (ICRA)

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Abstract-This paper presents a Therapist-in-the-Loop (TIL) framework for robotics-assisted mirror rehabilitation therapy integrated with adaptive Assist-as-Needed (ANN) training, to be adjusted based on the impairment and disability level of the patient's affected limb. Closed-loop system stability has been investigated using a combination of the Circle Criterion and the Small-Gain Theorem to account both for time-delay and the time-varying adaptive ANN training. Experiments to investigate the performance of the proposed framework are reported.

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“…Assumption 2 is a relaxed version of similar assumptions used in Polushin et al (2009). As shown in Polushin et al (2009), it does not impose any restrictions on characteristics of the communication channel, and can always be satisfied in real-life networks unless the communication is totally lost on a semi-infinite time interval.…”

Section: Assumption 2 the Communication Delays τmentioning

confidence: 99%

“…As shown in Polushin et al (2009), it does not impose any restrictions on characteristics of the communication channel, and can always be satisfied in real-life networks unless the communication is totally lost on a semi-infinite time interval. Now, let us denote Γ := Γ u • M ∈ G p×p , where…”

Section: Assumption 2 the Communication Delays τmentioning

confidence: 99%

“…Also, in teleoperator systems, stability with required gain usually cannot be achieved globally, which implies that an appropriate version of the small-gain theorem must admit stability properties of subsystems to be satisfied within a compact subset of state space and a compact range of inputs rather than globally (which corresponds to stability with finite restrictions as well as bounded domain of small-gain conditions). Although a number of nonlinear small-gain theorems presented in the literature addressed some of the above described issues (see, for example, (Dashkovskiy et al (2007); Karafyllis and Jiang (2009);Tiwari et al (2009);Dashkovskiy et al (2010)) for small gain conditions for interconnection of multiple subsystems, (Tiwari et al (2009)) for the case of bounded communication delays, (Polushin et al (2009)) for the case of discontinuous time-varying unbounded communication delays, and (Teel (1996); Polushin et al (2009)) for the case of finite restrictions), no small-gain results exist that would directly fit the specific restrictions of the networked cooperative bilateral teleoperator systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Small Gain Framework for Networked Cooperative Teleoperation

Polushin

2010

IFAC Proceedings Volumes

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A small gain approach for stability analysis of cooperative network-based force reflecting teleoperator systems is presented. The approach is based on a new version of inputto-output stability (IOS) nonlinear small gain theorem that is applicable to stability analysis of large-scale network-based interconnections. Using the small-gain theorem presented, we show that stability of the cooperative teleoperator system can always be achieved by choosing some of the system' gains appropriately.

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A Multichannel IOS Small Gain Theorem for Systems With Multiple Time-Varying Communication Delays

Cited by 60 publications

References 16 publications

Input-to-state stability analysis for interconnected difference equations with delay

Input-to-state stability analysis for interconnected difference equations with delay

Therapist-in-the-Loop robotics-assisted mirror rehabilitation therapy: An Assist-as-Needed framework

A Small Gain Framework for Networked Cooperative Teleoperation

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