Robust H/sub ∞/ filtering of stationary continuous-time linear systems with stochastic uncertainties

Gershon, Eli; Limebeer, D.J.N.; Shaked, U.; Yaesh, I.

doi:10.1109/9.964692

Cited by 149 publications

(103 citation statements)

References 10 publications

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“…This optimal linear filter was further analyzed by Tugnait [8], who noted that error turns out to be stable only in situations when the system is stable. Kalman filtering with multiplicative noise was studied in [9], [10], [11], however these works were also limited to stable systems.…”

Section: Introductionmentioning

confidence: 99%

Non-coherence in estimation and control

Ranade

Sahai

2013

2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-Control strategies for systems with information bottlenecks often follow an estimate-then-control paradigm. This paper presents a "non-coherent" system where this strategy cannot work and provides an alternative.The paper considers the estimation and control of a discretetime linear system with continuous random observation gain, i.e. through a non-coherent channel. It is shown that such an unstable system is not mean-squared observable regardless of the density of the random observation gain: the mean-squared estimation error for any estimator must go to infinity. This is surprising in the context of threshold results for rate-limited estimation.In contrast to other results with rate-limited feedback, the paper shows that the system can be closed-loop mean-square stabilized in a certain parameter regime even though its open-loop counterpart is not mean-square observable. Finally, carry-free models (generalized deterministic models) provide an intuitive interpretation for the results.

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Section: Introductionmentioning

confidence: 99%

Non-coherence in estimation and control

Ranade

Sahai

2013

2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…Much work has been done for H ∞ filtering problem, see e.g. [1,3,10,11,[22][23][24] and references therein. It has also been well recognized that time delay exists commonly in dynamic systems and is frequently a source of instability and poor performance.…”

Section: Introductionmentioning

confidence: 99%

Filtering for uncertain 2-D discrete systems with state delays

Wang

Gao

et al. 2007

Signal Processing

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This paper is concerned with the problem of robust H ∞ filtering for two-dimensional (2-D) discrete systems with time delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini-Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H ∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.

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“…For instance, the problem of H ∞ filtering has been addressed for linear systems [9], linear systems with uncertain parameters [18], [22], delay systems [13], [23], and stochastic systems [16], [33]. It is noted that although H ∞ filtering offers robustness that is significantly better than Kalman filtering [1], [19] (also called H 2 filtering), H ∞ filtering is so conservative that it often leads to a large intolerable estimation error variance when the system is driven by white noise signals.…”

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 H/sub ∞/ filtering of stationary continuous-time linear systems with stochastic uncertainties

Cited by 149 publications

References 10 publications

Non-coherence in estimation and control

Non-coherence in estimation and control

Filtering for uncertain 2-D discrete systems with state delays

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

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