$${\cal{H}}_{\infty}$$ and $${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$$ Model Reduction for System Input with Sector Nonlinearities

Lam, James; Gao, Huijun; Xu, Shengyuan; Wang, C.

doi:10.1007/s10957-004-1714-6

Cited by 78 publications

(32 citation statements)

References 18 publications

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“…The nonlinear description in (4) is quite general that include the usual Lipschitz conditions as a special case. Note that both the control analysis and model reduction problems for systems with sector nonlinearities have been intensively studied; see, e.g., [9] and [15].…”

Section: Problem Formulationmentioning

confidence: 99%

Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

Dong

Wang²,

Gao

2010

IEEE Trans. Signal Process.

272

107

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Abstract-In this paper, the robust filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts. A sequence of random variables, all of which are mutually independent but obey Bernoulli distribution, are introduced to account for the randomly occurred communication delays. The packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. The discrete-time system under consideration is also subject to parameter uncertainties, state-dependent stochastic disturbances and sector-bounded nonlinearities. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the performance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed performance for the overall filtering error dynamics, in the presence of random delays, random dropouts, nonlinearities, and the parameter uncertainties. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is given for the desired filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper.Index Terms-Networked systems, nonlinear systems, packet dropout, robust filtering, stochastic systems, stochastic time-varying communication delays.

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Section: Problem Formulationmentioning

confidence: 99%

Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

Dong

Wang²,

Gao

2010

IEEE Trans. Signal Process.

272

107

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“…Note that both the control analysis and model reduction problems for systems with sector nonlinearities have been intensively studied, see e.g. [9,13,14].…”

Section: Problem Formulationmentioning

confidence: 99%

“…The system under study involves parameter uncertainties, Itô-type stochastic disturbances, time-varying delays and inherent sector-like nonlinearities. Note that, among different descriptions of the nonlinearities, the so-called sector nonlinearity [12] has gained much attention for deterministic systems, and both the control analysis and model reduction problems have been investigated, see [9,13,14]. We first investigate the sufficient conditions for the filtering error system to be stable in the mean square, and then derive the explicit expression of the desired controller gains.…”

Section: Introductionmentioning

confidence: 99%

H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities

2008

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In this paper, we deal with the robust H ∞ filtering problem for a class of uncertain nonlinear time-delay stochastic systems. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, timevarying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed H ∞ disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô's differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived.

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“…Note that both the control analysis and model reduction problems for systems with sector nonlinearities have been intensively studied, see e.g. [9][10][11].…”

Section: Remarkmentioning

confidence: 99%

“…Most recently, in [7], an H 1 -type theory has been developed for a large class of discrete-time nonlinear stochastic systems. It is worth mentioning that, among different descriptions of the nonlinearities, the so-called sector nonlinearity [8] has gained much attention for deterministic systems, and both the control analysis and model reduction problems have been investigated, see [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Robust H_∞ control for a class of nonlinear stochastic systems with mixed time delay

Liu

Wang

Liu

2007

Intl J Robust & Nonlinear

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SUMMARYThis paper is concerned with the problem of robust H 1 control for a class of uncertain nonlinear Itoˆ-type stochastic systems with mixed time delays. The parameter uncertainties are assumed to be norm bounded, the mixed time delays comprise both the discrete and distributed delays, and the sector nonlinearities appear in both the system states and delayed states. The problem addressed is the design of a linear state feedback controller such that, in the simultaneous presence of parameter uncertainties, system nonlinearities and mixed time delays, the resulting closed-loop system is asymptotically stable in the mean square and also achieves a prescribed H 1 disturbance rejection attenuation level. By using the Lyapunov stability theory and the Itoˆdifferential rule, some new techniques are developed to derive the sufficient conditions guaranteeing the existence of the desired feedback controllers. A unified linear matrix inequality is proposed to deal with the problem under consideration and a numerical example is exploited to show the usefulness of the results obtained.

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$${\cal{H}}_{\infty}$$ and $${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$$ Model Reduction for System Input with Sector Nonlinearities

Cited by 78 publications

References 18 publications

Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities

Robust H_∞ control for a class of nonlinear stochastic systems with mixed time delay

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$${\cal{H}}_{\infty}$$ and $${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$$ Model Reduction for System Input with Sector Nonlinearities

Cited by 78 publications

References 18 publications

Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities

Robust H∞ control for a class of nonlinear stochastic systems with mixed time delay

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Robust H_∞ control for a class of nonlinear stochastic systems with mixed time delay