Robust /spl Hscr//sub 2/ filtering for discrete-time uncertain linear systems using parameter-dependent Lyapunov functions

Barbosa, Karina A.; Souza, Carlos E. de; Trofino, Alexandre

doi:10.1109/acc.2002.1025287

Cited by 23 publications

(21 citation statements)

References 5 publications

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“…This interiorpoint method for convex optimization has also been used to recursively compute the minimal confidence ellipsoid for the state in [14]. The LMI approach has been applied to solve the robust H 2 and H ∞ filtering for systems with norm-bounded uncertainty, integral quadratic constraints and polytopic uncertainty, see [4], [5], [14], [15] and [16]- [17]. A problem with both deterministic (unknown-but-bounded) and stochastic uncertainties has been considered in [11], [18], [19]- [20] and more recently in [21].…”

Section: Introductionmentioning

confidence: 99%

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

Ponomareva

Date

2014

Applied Mathematical Modelling

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An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the 'perturbed Kalman filter' (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified.

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Section: Introductionmentioning

confidence: 99%

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

Ponomareva

Date

2014

Applied Mathematical Modelling

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“…First, we give the following theorem. (1) and the filter with the form of (3), given a scalar α ∈ R + . There exist the filter matrices A f , B f , C f and the matrix P (ρ) > 0,…”

Section: Parameter-dependent Lyapunov Approachmentioning

confidence: 99%

“…In the past few years, there have been many attempts to reduce this design conservatism. In [1], a Lyapunov function which is a linear or quadratic function of the uncertain parameter vector has been developed. In [10,14], an additional parameter-dependent matrix variable has been introduced which allows the Lyapunov function to be vertex dependent.…”

Section: Introductionmentioning

confidence: 99%

Convex Optimization Approaches to Robust ℒ1 Fixed-Order Filtering for Polytopic Systems with Multiple Delays

Lam

Luo

2008

Circuits Syst Signal Process

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This paper investigates the robust L 1 fixed-order filtering problem for continuous polytopic systems with multiple state delays. Attention is focused on the design of robust full-order and reduced-order filters that guarantee the filtering error system to be asymptotically stable and satisfy the worst case peak-to-peak gain of the filtering error system for all admissible uncertainties and time delays. In particular, we concentrate on the delay-dependent case, and the peak-to-peak performance criterion is first established for polytopic systems with multiple state delays. Two different convex optimization approaches are proposed to solve this problem. One is the parameter-dependent Lyapunov approach in which the filter is not only dependent on the parameters (residing in a polytope), but also the Lyapunov matrices are different over the entire polytope domain. The other is the quadratic stability approach which obtains an admissible filter in the quadratic framework. Computational algorithms in terms of linear matrix inequalities (LMIs) are provided. It is shown that the parameter-dependent Lyapunov approach turns out to be less conservative than the quadratic stability approach, but the quadratic stability approach is computationally less demanding. Two numerical examples are presented to illustrate the proposed theory.

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“…This is due to the fact that the same Lyapunov function is used to assure the robust stability of the system for the entire uncertainty domain. In order to overcome this conservativeness, recently, a number of results on the stability analysis and control synthesis of uncertain systems based on the basisdependent Lyapunov function approach have appeared in [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Especially, the problem of output feedback control for linear systems with time-varying uncertainties was investigated in [9,11,17,18].…”

Section: Introductionmentioning

confidence: 99%

H ∞ controller design for linear systems with time-invariant uncertainties

Chang

2011

Int. J. Control Autom. Syst.

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This paper considers the problem of designing robust H ∞ state feedback controller for linear continuous-time systems with time-invariant uncertainties. The main result given here concerns H ∞ controller design using the parameter dependent Lyapunov function approach and a new control law. A new condition ensuring the linear systems to be is asymptotically stable with a prescribed H ∞ performance is proposed in terms of a set of linear matrix inequalities (LMIs). Theoretic proof is given to show that the proposed condition is less conservative than existing results in the literature. An example is provided to demonstrate the efficiency of the proposed method.

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Robust /spl Hscr//sub 2/ filtering for discrete-time uncertain linear systems using parameter-dependent Lyapunov functions

Cited by 23 publications

References 5 publications

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

An exact minimum variance filter for a class of discrete time systems with random parameter perturbations

Convex Optimization Approaches to Robust ℒ1 Fixed-Order Filtering for Polytopic Systems with Multiple Delays

H ∞ controller design for linear systems with time-invariant uncertainties

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