Robust ℋ/sub ∞/ filtering for a class of linear parameter-varying systems

Mahmoud, Magdi S.; Boujarwah, A. S.

doi:10.1109/81.948442

Cited by 35 publications

(12 citation statements)

References 11 publications

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“…As follows from Theorem 3 from [1] and Theorem 1 in [2], the optimal mean-module estimate equations for the error states (13) and (15) are given bẏ…”

Section: Design Of Central Energy-to-peak Filtermentioning

confidence: 99%

Central energy-to-peak filter design for uncertain linear systems

Serna

Lopez-Hernandez

2013

2013 9th Asian Control Conference (ASCC)

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This paper presents the central finite-dimensional energy-to-peak filter for linear systems that is optimal with respect to a modified Bolza-Meyer quadratic criterion including the first degree state-dependent term and the attenuation control term with the opposite sign. The obtained solution is based on reducing the original energy-to-peak filtering problem to the corresponding mean-module filtering problem, using the technique proposed in [1]. The paper first presents the central energy-to-peak filter for linear systems, based on the optimal mean-module filter from [2], assuming the standard filtering conditions of stabilizability, detectability, and noise orthonormality. Finally, to relax the standard conditions, the paper presents the generalized version of the designed energyto-peak filter in the absence of the noise orthonormality. Numerical simulations are conducted to verify performance of the designed energy-to-peak filter for linear systems against the central suboptimal H ∞ filter [3]. The simulation results show a definite advantage in the values of the noise-output energy-topeak norm in favor of the designed filter.

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“…As follows from Theorem 3 from [1] and Theorem 1 in [2], the optimal mean-module estimate equations for the error states (13) and (15) are given bẏ…”

Section: Design Of Central Energy-to-peak Filtermentioning

confidence: 99%

Central energy-to-peak filter design for uncertain linear systems

Serna

Lopez-Hernandez

2013

2013 9th Asian Control Conference (ASCC)

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“…The H 1 controller design implies that the resulting closedloop control system is robustly stable and achieves a prescribed level of attenuation from the disturbance input to the output in L 2 /l 2 -norm. A large number of results on this subject have been reported for systems in the general situation, linear or nonlinear (Van der Schaft 1991, 1992Wang, Xie, and De Souza 1992;Xie, Shi, and De Souza 1993;Chen and Tseng 1994;Katebi and Zhang 1995;Nguang 1997;Shi, Shue, Shi, and Agarwal 1999;Fridman 2001;Mahmoud and Boujarwah 2001;Guo and Lam 2002;Gao, Lam, and Wang 2002;Xu and Chen 2002;Xu, Lu, Zhou, and Yang 2004;Hsiao 2007;Mahmoud, Shi, Boukas, and Jain 2008;Xia, Qiu, Zhang, Gao, and Wang 2008;Wang, Ho, Liu, and Liu 2009;Xia, Fu, Shi, Wu, and Zhang 2009;Zhang and Boukas 2009;Zhang and Shi 2009;Zhang, Wang, and Chen 2009). The sufficient conditions for the existence of an H 1 controller, where the control and filter gain matrices satisfy Riccati equations, were obtained for linear systems in Doyle et al (1989).…”

Section: Introductionmentioning

confidence: 95%

Central suboptimalH_∞controller design for linear time-varying systems with unknown parameters

Soto

Calderon-Alvarez

2011

International Journal of Systems Science

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This article presents the central finite-dimensional H 1 controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H 1 controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), 'State-space Solutions to Standard H 2 and H Infinity Control Problems', IEEE Transactions Automatic Control, 34, 831-847]. This article yields the central suboptimal H 1 controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), 'Optimal LQG Controller for Linear Systems with Unknown Parameters', Journal of The Franklin Institute, 345, 293-302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H 1 controller for linear systems with exactly known parameter values.

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“…From this perspective, robust filtering can be viewed as an extension of the celebrated Kalman filter [1] to uncertain dynamical systems. The past decade has witnessed major developments in robust filtering problem using various approaches [3,[17][18][19][20]23]. Research into H ∞ filtering for singular systems and related results is available in [15,26,28].…”

Section: Introductionmentioning

confidence: 99%

Stability and implementable ℋ∞ filters for singular systems with nonlinear perturbations

Mahmoud

Almutairi

2008

Nonlinear Dyn

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In this paper, we investigate the problem of designing H ∞ filter for a class of continuous-time uncertain singular systems with nonlinear perturbations, which can be realized in practice. The perturbation is a time-varying function of the system state and satisfies a Lipschitz constraint. The design objective is to guarantee that a prescribed upper bound on an H ∞ performance of the robust filter is attained for all possible energy-bounded input disturbances and all admissible uncertainties and which can be implemented on-line to get a good replica of the state. We first establish sufficient condition for the existence and uniqueness of solution to the singular system connected with the normal filter. Using a linear matrix inequality (LMI) format, we then provide a sufficient condition for the asymptotic stability of the realizable H ∞ filter. Then by means of a convex analysis procedure the filter gain matrices are derived and an important special case is readily deduced. Finally, a numerical example is presented to illustrate the theoretical developments. M.S. Mahmoud ( ) Systems Engineering Department,

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Robust ℋ/sub ∞/ filtering for a class of linear parameter-varying systems

Cited by 35 publications

References 11 publications

Central energy-to-peak filter design for uncertain linear systems

Central energy-to-peak filter design for uncertain linear systems

Central suboptimalH_∞controller design for linear time-varying systems with unknown parameters

Stability and implementable ℋ∞ filters for singular systems with nonlinear perturbations

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Robust ℋ/sub ∞/ filtering for a class of linear parameter-varying systems

Cited by 35 publications

References 11 publications

Central energy-to-peak filter design for uncertain linear systems

Central energy-to-peak filter design for uncertain linear systems

Central suboptimalH∞controller design for linear time-varying systems with unknown parameters

Stability and implementable ℋ∞ filters for singular systems with nonlinear perturbations

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Central suboptimalH_∞controller design for linear time-varying systems with unknown parameters