Nonlinear observation over erasure channel

Diwadkar, Amit; Vaidya, Umesh

doi:10.1109/cdc.2010.5717551

Cited by 9 publications

(20 citation statements)

References 24 publications

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“…, Ξ(t)}. Proof: The proof uses Mean Value Theorem for vector valued functions and Fatou's Lemma and is on similar lines to the proof in [23]. We now use some properties of graph Laplacian to simplify the system equation (13).…”

Section: Resultsmentioning

confidence: 94%

“…Proof: This follows from equation (17) and necessary condition for exponential mean square stability proved in [23] Lemma 10. We now give the proof for the different cases for the stochastic coupling given in Theorem 6 and 7.…”

Section: Resultsmentioning

confidence: 94%

“…The error equation in (6) resembles the observer error equation with s(t) being the true state andx the estimated states. In [23], the problem of nonlinear observation over analog erasure channel, modeled as a Bernoulli random variable, is studied. In particular, the main results of [23] (Theorem 10) provides necessary condition for the mean square exponential stabilziation of the observer error dynamics.…”

Section: Resultsmentioning

confidence: 99%

“…In [23], the problem of nonlinear observation over analog erasure channel, modeled as a Bernoulli random variable, is studied. In particular, the main results of [23] (Theorem 10) provides necessary condition for the mean square exponential stabilziation of the observer error dynamics. This resemblence between the synchronization problem and the observation problem will now be used to prove the two main results of this paper.…”

Section: Resultsmentioning

confidence: 99%

“…Following the proof in [23], it can be shown that the necessary condition for the existence of optimal matrix Lyapunov function P(s(t)) that satisfies above inequality is given by…”

Section: Proof Of Theorem 6 For Single Link Switchingmentioning

confidence: 97%

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Robust synchronization in nonlinear network with link failure uncertainty

Diwadkar

Vaidya

2011

IEEE Conference on Decision and Control and European Control Conference

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The problem of synchronization of systems over a network, is a widely studied problem given the importance of synchronization phenomena, in various natural science and engineering applications. In this paper, we study one of the important aspect of this problem that is, robustness of synchronization to random link failure uncertainty. The link failure uncertainty is modeled as an on-off Bernoulli switch. The main results of this paper provide, for the first time, analytical conditions for the maximum tolerable link failure uncertainty to maintain mean square synchronization among the network components. The analytical conditions are expressed in terms of individual component dynamics, network properties, and link uncertainty. The main results of this paper can be used to determine, the weakest/strongest link in the network. Simulation results are provided to verify the main results of this paper.

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Section: Resultsmentioning

confidence: 94%

Section: Resultsmentioning

confidence: 94%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Following the proof in [23], it can be shown that the necessary condition for the existence of optimal matrix Lyapunov function P(s(t)) that satisfies above inequality is given by…”

Section: Proof Of Theorem 6 For Single Link Switchingmentioning

confidence: 97%

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Robust synchronization in nonlinear network with link failure uncertainty

Diwadkar

Vaidya

2011

IEEE Conference on Decision and Control and European Control Conference

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Stabilization of linear time varying systems over uncertain channels

Diwadkar

Vaidya

2012

Int. J. Robust Nonlinear Control

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SUMMARYIn this paper, we study the problem of control of discrete‐time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the closed‐loop system as a stability criterion. We show that fundamental limitations arise for the mean square exponential stabilization for the closed‐loop system expressed in terms of statistics of channel uncertainty and the positive Lyapunov exponent of the open‐loop uncontrolled system. Our results generalize the existing results known in the case of linear time invariant systems, where Lyapunov exponents are shown to emerge as the generalization of eigenvalues from linear time invariant systems to linear time varying systems. Simulation results are presented to verify the main results of this paper. Copyright © 2012 John Wiley & Sons, Ltd.

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