9. A Linear Matrix Inequality Approach to the Design of Robust H<sub>2</sub> Filters

Souza, Carlos E. de; Trofino, Alexandre

doi:10.1137/1.9780898719833.ch9

Cited by 57 publications

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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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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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“…where A i , B i , C i , and D i , i = 1, … , m, are given matrices [15]. In the case of m = 1, the system matrix M is perfectly known.…”

Section: Problem Formulationmentioning

confidence: 99%

Robust proportional-integral Kalman filter design using a convex optimization method

2008

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This paper proposes a design approach to the robust proportional-integral Kalman filter for stochastic linear systems under convex bounded parametric uncertainty, in which the filter has a proportional loop and an integral loop of the estimation error, providing a guaranteed minimum bound on the estimation error variance for all admissible uncertainties. The integral action is believed to increase steady-state estimation accuracy, improving robustness against uncertainties such as disturbances and modeling errors. In this study, the minimization problem of the upper bound of estimation error variance is converted into a convex optimization problem subject to linear matrix inequalities, and the proportional and the integral Kalman gains are optimally chosen by solving the problem. The estimation performance of the proposed filter is demonstrated through numerical examples and shows robustness against uncertainties, addressing the guaranteed performance in the mean square error sense.

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“…There are essentially two approaches to the robust estimation problem. The first is robust H 2 filtering, which minimizes the upper bound of the estimation error variance for all possible parametric uncertainties under the assumption that the noise processes have known power spectral densities [4,9]. In many practical situations, however, we may not be able to have exactly known information on the spectral densities of the noise processes.…”

Section: Introductionmentioning

confidence: 99%

Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach

Lam

2009

Circuits Syst Signal Process

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This paper is concerned with the H ∞ filtering problem for a continuoustime linear switched system with time-varying delay in its state. To reduce the overdesign of the quadratic framework, this paper proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. By using an average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability with a weighted H ∞ performance for the filtering error system with the decay estimate explicitly given. Then, the corresponding solvability condition for a desired filter is established, and the filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical software. All the conditions obtained in this paper are delay dependent. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.

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9. A Linear Matrix Inequality Approach to the Design of Robust H₂ Filters

Cited by 57 publications

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Filtering for uncertain 2-D discrete systems with state delays

Filtering for uncertain 2-D discrete systems with state delays

Robust proportional-integral Kalman filter design using a convex optimization method

Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach

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9. A Linear Matrix Inequality Approach to the Design of Robust H2 Filters

Cited by 57 publications

References 0 publications

Filtering for uncertain 2-D discrete systems with state delays

Filtering for uncertain 2-D discrete systems with state delays

Robust proportional-integral Kalman filter design using a convex optimization method

Weighted H ∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach

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9. A Linear Matrix Inequality Approach to the Design of Robust H₂ Filters