Robust energy-to-peak filtering with improved LMI representations

Gao, Huijun; Wang, C.

doi:10.1049/ip-vis:20030235

Cited by 51 publications

(37 citation statements)

References 15 publications

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“…As can be seen in Assumption 2.2, the parameter uncertainties are assumed to be of the polytopic type, entering into all the matrices of the system model. The polytopic uncertainty has been widely used in studies on the problems of robust control and filtering for uncertain systems (see, e.g., [5,7,9]), and many practical systems possess parameter uncertainties which can be either exactly modeled or overbounded by the polytope ℜ. In addition, the nonlinear disturbance in Assumption 2.1 has also been widely used in the literature (see, e.g., [4,10,11]).…”

Section: Problem Formulationmentioning

confidence: 99%

“…The way in which the proof of the theorem can be carried out is similar to that for the proof of Theorem 4 in [7] and is therefore, omitted here. Theorem 3.2.…”

Section: Delay-dependent Approachmentioning

confidence: 99%

“…For such cases, H ∞ filtering was introduced in 1989 [6], where the input signal is assumed to be energy bounded and the main objective is to minimize the H ∞ norm of the filtering error system. Other performance indexes introduced for systems with partially known noise information are l 2 -l ∞ (energy-to-peak) [7] and l 1 (peak-to-peak) [8], which have different physical meanings when used as performance indexes for filtering error systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lmi Approach to Robust Filtering for Discrete Time-Delay Systems With Nonlinear Disturbances

Gao

Wang

2008

Asian Journal of Control

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This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete-time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H ∞ or l 2 -l ∞ sense with respect to all energy-bounded noise disturbances for all admissible uncertainties and time delays. Both delay-dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.

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Section: Problem Formulationmentioning

confidence: 99%

“…The way in which the proof of the theorem can be carried out is similar to that for the proof of Theorem 4 in [7] and is therefore, omitted here. Theorem 3.2.…”

Section: Delay-dependent Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lmi Approach to Robust Filtering for Discrete Time-Delay Systems With Nonlinear Disturbances

Gao

Wang

2008

Asian Journal of Control

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“…A stability and L 2 gain analysis for switched linear systems with time delay was considered in [24]. On the other hand, the l 2 − l ∞ performance was first proposed in [22]; one can refer to [3], [4], [5] and the references therein for its further extension. In contrast with the great number of results obtained for stability and L 2 performance, to the best of our knowledge, the l 2 − l ∞ control problem for discrete-time switched systems, especially for switched systems with both parametric uncertainties and time delays, has not been fully investigated yet.…”

Section: Introductionmentioning

confidence: 99%

Robust l2 - l∞ Control for Uncertain Discrete-Time Switched Systems with Delays

Jiang

Shi

et al. 2006

Circuits Syst Signal Process

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This paper is concerned with the problem of robust l 2 − l ∞ control for uncertain discrete-time switched systems with time delay in the state. The uncertainty is assumed to be of structured linear fractional form which includes the norm-bounded uncertainty as a special case. The control design approach is facilitated by introducing some additional instrumental matrix variables. The additional matrix variables decouple the Lyapunov and system matrices, which make the control design feasible. The proposed approach leads to less conservativeness of previous design methods, and the results also generalize earlier works for a more general parametric uncertainty structure. A numerical example is also given to demonstrate the effectiveness and the potential of the proposed techniques.

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“…Very recently, the parameter-dependent stability idea was also utilized by some researchers to investigate the filtering problem for uncertain systems; see for instance, [12], [15], [30]. In the present work, we attempt to investigate the mixed H 2 /H ∞ filtering problem for a class of uncertain linear continuous-time systems with parameters residing in a polytope.…”

Section: Introductionmentioning

confidence: 99%

Mixed H2/H∞ Filtering for Continuous-Time Polytopic Systems: A Parameter-Dependent Approach

Gao

Lam

Wang

2005

Circuits Syst Signal Process

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The problem of mixed H 2 /H ∞ filtering is investigated for continuous-time polytopic systems. Given a stable system whose parameters reside in a polytope and can be measured online, attention is focused on the design of parameter-dependent filters such that the filtering error system is asymptotically stable and has guaranteed H 2 and H ∞ performances with respect to different input signals. By introducing multiple Lyapunov functions, the parameter-dependent approach developed in this paper is able to yield much less conservative filters than the existing results. A numerical example is provided to show the effectiveness and reduced conservatism of the proposed theory.

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Robust energy-to-peak filtering with improved LMI representations

Cited by 51 publications

References 15 publications

Lmi Approach to Robust Filtering for Discrete Time-Delay Systems With Nonlinear Disturbances

Lmi Approach to Robust Filtering for Discrete Time-Delay Systems With Nonlinear Disturbances

Robust l2 - l∞ Control for Uncertain Discrete-Time Switched Systems with Delays

Mixed H2/H∞ Filtering for Continuous-Time Polytopic Systems: A Parameter-Dependent Approach

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