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This paper proposes a new approach based on parameter-dependent linear matrix inequality (LMI) conditions associated with a scalar parameter that are sufficient to provide robust H 2 and H ∞ reduced-order mode-dependent, partially mode-dependent or mode-independent filters for discrete-time Markov jump linear systems (MJLS) with time-invariant uncertain transition probabilities. Time-invariant uncertainties in the state–space matrices of the modes can be handled as well. As main difference with respect to the existing approaches in the literature, the filter matrices are obtained directly from the slack variables introduced in the conditions. Moreover, the proposed conditions become also necessary for a particular choice of the scalar parameter when mode-dependent full-order filters are designed for systems without uncertainties. Additionally, for precisely known generalized Bernoulli jump systems (i.e., the case where all the rows of the transition probability matrix are equal), optimal solutions are obtained for both mode-dependent and mode-independent full-order filters. Examples (including one motivated by a practical application) are presented to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the robust estimation problem of a signal given noisy observations. We assume that the actual statistics of the signal and observations belong to a ball about the nominal statistics. This ball is formed by placing a bound on a suitable divergence (or distance) between the actual and the nominal statistics. Then, the robust estimator is obtained by minimizing the mean square error according to the least favorable statistics in that ball. Therefore, we obtain a divergence-based minimax approach to robust estimation. Choosing a set of divergences, called Tau divergence family, we show that the Bayes estimator based on the nominal statistics is the optimal solution. Moreover, in the dynamic case, the optimal offline estimator is the noncausal Wiener filter based on the nominal statistics. [ABSTRACT FROM AUTHOR]

In this paper we deal with an optimal filtering problem for uncertain discrete-time systems. Parametric uncertainties of the underlying model are assumed to be norm bounded. We propose an approach based on regularization and penalty function to solve this problem. The optimal robust filter with the respective recursive Riccati equation is written through unified frameworks defined in terms of matrix blocks. These frameworks do not depend on any auxiliary parameters to be tuned. Simulation results show the effectiveness of the robust filter proposed. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problem of robust finite frequency (FF) filtering for uncertain two-dimensional (2-D) discrete-time systems in the Fornasini–Marchesini local state-space (FM LSS) model with polytopic uncertain parameters. The goal of the paper is to design filters such that the FF norm of the filtering error system has a specified upper bound for all uncertainties. In light of a recently developed generalized bounded real lemma, a linear matrix inequality-based approach is proposed for robust FF filter analysis and design. It is demonstrated that the presented approach to robust FF filter design covers the latest standard filtering result. Moreover, it is shown that the existing results specialized for the Roesser model, when applied to the FM LSS model through a model transformation, are much more restrictive than the proposed results in the paper, further justifying this work. [Copyright &y& Elsevier]

Abstract: In this paper, robust optimal filtering is addressed for continuous-time stochastic systems with polytopic parameter uncertainty. A new robust stability condition is presented. A continuous-time robust optimal filter is obtained by solving a sufficient linear matrix inequality condition characterizing a solution of a robust minimum variance filtering problem which takes into account the polytopic type of model uncertainties. The proposed approach is demonstrated through numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the robust filtering problem for a class of uncertain nonlinear time-delay stochastic systems. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô’s differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived. [Copyright &y& Elsevier]

Abstract: In this paper a new approach to robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs. [Copyright &y& Elsevier]

Abstract: The notion of quadratic boundedness, which allows one to address the stability of a dynamic system in the presence of bounded disturbances, is applied to the design of state estimators for discrete-time linear systems with polytopic uncertainties. Necessary and sufficient stability conditions are stated and upper bounding sequences on the estimation error are derived. For the purpose of design, such conditions can be expressed in terms of linear matrix inequalities (LMIs), thus guaranteeing the numerical tractability. Simulation results are reported to show the effectiveness of the approach. [Copyright &y& Elsevier]