Robust H∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays

Xu, Shengyuan; Lam, James; Gao, Huijun; Zou, Yun

doi:10.1007/s00034-005-0921-1

Cited by 43 publications

(37 citation statements)

References 17 publications

(14 reference statements)

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“…In many physical, industrial and circuit systems, time delays occur due to the finite capability of information processing, data transmission among various parts of the systems and some essential simplification of the corresponding process models [9,27,29,37,39,49,[55][56][57]. The delaying effect is often detrimental to the performance, and even renders instability.…”

Section: Introductionmentioning

confidence: 99%

Model Order Reduction for Neutral Systems by Moment Matching

Wang

Lam

et al. 2012

Circuits Syst Signal Process

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Circuits with delay elements are very popular and important in the simulation of very-large-scale integration (VLSI) systems. Neutral systems (NSs) with multiple constant delays (MCDs), for example, can be used to model the partial element equivalent circuits (PEECs), which are widely used in high-frequency electromagnetic (EM) analysis. In this paper, the model order reduction (MOR) problem for the NS with MCDs is addressed by moment matching method. The nonlinear exponential terms coming from the delayed states and the derivative of the delayed states in the transfer function of the original NS are first approximated by a Padé approximation or a Taylor series expansion. This has the consequence that the transfer function of the original NS is exponential-free and the standard moment matching method for reduction is readily applied. The Padé approximation of exponential terms gives an expanded delay-free system, which is further reduced to a delay-free reduced-order model (ROM). A Taylor series expansion of exponential terms lets the inverse in the original transfer function have only powers-of-s terms, whose coefficient matrices are of the same size as the original NS, which results in a ROM modeled by a lower-order NS. Numerical examples are included to show the effectiveness of the proposed al-

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Section: Introductionmentioning

confidence: 99%

Model Order Reduction for Neutral Systems by Moment Matching

Wang

Lam

et al. 2012

Circuits Syst Signal Process

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“…The complete classification of the "general situation" cases (this means that there are no special assumptions on the structure of state and observation equations and the initial conditions), where the nonlinear finite-dimensional filter exists, is given in Yau (1994). There also exists an extensive bibliography on robust, in particular, H ∞ filtering for linear (Xu and Chen (2003), Mahmoud and Shi (2003) and Xu et al (2005)) and nonlinear (Xie et al (1996), Nguang and Fu (1996), Fridman and Shaked (1997), Shi (1998), Fleming and McEneaney (2001), Yaz and Yaz (2001), Xu and van Dooren (2002), Wang et al (2003), Gao and Wang (2004), Zhang et al (2005), Gao et al (2005), Zhang et al (2007), Gao and Chen (2007), Wang et al (2008), Wang et al (2009), Wei et al (2009) and Shen et al (2009)) stochas-tic systems. Apart form the "general situation," the mean-square finite-dimensional filters have been designed for certain classes of polynomial system states with Gaussian noises over linear observations (Basin (2008), Basin et al (2008) and Basin et al (2009)) and a few results related to nonlinear Poisson systems can be found in Lu et al (2001), Kolmanovsky and Maizenberg (2002a), Hannequin and Mas (2002), Kolmanovsky and Maizenberg (2002b), Zhang et al (2008a), Dupé et al (2008), Zhang et al (2008b), and Basin and Maldonado (2011).…”

Section: Introductionmentioning

confidence: 99%

ean-Square Filtering for Polynomial System States Confused with Poisson Noises over Polynomial Observations

Maldonado¹,

Karimi

2011

MIC

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In this paper, the mean-square filtering problem for polynomial system states confused with white Poisson noises over polynomial observations is studied proceeding from the general expression for the stochastic Ito differentials of the mean-square estimate and the error variance. In contrast to the previously obtained results, the paper deals with the general case of nonlinear polynomial states and observations with white Poisson noises. As a result, the Ito differentials for the mean-square estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining an approximate closed-form finite-dimensional system of the filtering equations for any polynomial state over observations with any polynomial drift is then established. In the example, the obtained closed-form filter is applied to solve the third order sensor filtering problem for a quadratic state, assuming a conditionally Poisson initial condition for the extended third order state vector. The simulation results show that the designed filter yields a reliable and rapidly converging estimate.

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“…The H ∞ filter design implies that the resulting closed-loop filtering system is robustly stable and achieves a prescribed level of attenuation from the disturbance input to the output estimation error in the L 2 /l 2 -norm. Numerous results on this subject have been reported for systems in the general situation, linear or nonlinear (see [23,25,27,45,47,62,65,66,71]). For the specific area of linear time-delay systems, the H ∞ filtering problem has also been extensively studied (see [12, 21, 22, 24, 25, 28, 29, 33, 35, 40, 43, 56, 57, 59, 61, 63-66, 69, 72, 74]).…”

Section: Introductionmentioning

confidence: 99%

Central Suboptimal H ∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay

Basin

Shi

Calderon-Alvarez

et al. 2008

Circuits Syst Signal Process

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This paper presents central finite-dimensional H ∞ filters for linear systems with state or measurement delay that are suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including an attenuation control term with opposite sign. In contrast to the results previously obtained for linear time-delay systems, the paper reduces the original H ∞ filtering problems to H 2 (optimal mean-square) filtering problems, using the technique proposed in Doyle et al. (IEEE Trans. Automat. Contr. AC-34:831-847, 1989). The paper first presents a central suboptimal H ∞ filter for linear systems with state delay, based on the optimal H 2 filter from Basin et al. (IEEE Trans. Automat. Contr. AC-50:684-690, 2005), which contains a finite number of filtering equations for any fixed filtering horizon, but this number grows unboundedly as time goes to infinity. To overcome that difficulty, an alternative central suboptimal H ∞ filter is designed for linear systems with 306 Circuits Syst Signal Process (2009) 28: 305-330 state delay, which is based on the alternative optimal H 2 filter from Basin et al. (Int. J. Adapt. Control Signal Process. 20(10):509-517, 2006). Then, the paper presents a central suboptimal H ∞ filter for linear systems with measurement delay, based on the optimal H 2 filter from Basin and Martinez-Zuniga (Int. J. Robust Nonlinear Control 14(8): [685][686][687][688][689][690][691][692][693][694][695][696] 2004). Numerical simulations are conducted to verify the performance of the designed three central suboptimal filters for linear systems with state or measurement delay against the central suboptimal H ∞ filter available for linear systems without delays.

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Robust H∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays

Cited by 43 publications

References 17 publications

Model Order Reduction for Neutral Systems by Moment Matching

Model Order Reduction for Neutral Systems by Moment Matching

ean-Square Filtering for Polynomial System States Confused with Poisson Noises over Polynomial Observations

Central Suboptimal H ∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay

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