Robust Filtering for Discrete-Time Linear Parameter-Varying Descriptor Systems (original) (raw)
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2013 10th IEEE International Conference on Control and Automation (ICCA), 2013
This paper addresses the problems of admissibility and H∞ performance analysis for continuous-time linear time-varying (LTV) descriptor systems. Firstly, necessary and sufficient conditions are proposed to ascertain the admissibility of LTV descriptor systems based on the Lyapunov theory. Secondly, admissibility and H∞ performance analysis results are derived to deal with linear parameter-varying descriptor systems, where the parameters and their time-derivatives are supposed to be bounded with known limits. These results are then cast in terms of parameter-dependent strict linear matrix inequalities (LMIs) considering affine and polynomial parameter-dependent Lyapunov functions. A numerical example illustrates the proposed approach.
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2006
LESSI, Département de Physique Faculté des Sciences Dhar El Mehraz B.P : 1796, 30000 Fes-Atlas Morocco. E-mail: hmamed_a@fsdmfes.ac.ma E-mail: elhafidchelliq@caramail.com . Abstract AA New robust sufficient stability condition for uncertain continuous-time systems with convex polytopic uncertainty are given. They enable to check stability using parameterdependent Lyapunov functions which are derived from LMI conditions. A descriptor system approach is taken to deriving linear matrix inequality LMIs conditions. The proposed conditions are less restrictive than other parameter dependent based methods from the literature providing better results as illustrated by means of numerical examples. The reduction of the conservatism is illustrated by a numerical evaluation.
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This paper deals with the problems of robust stability and stabilization for uncertain continuous descriptor systems. We propose a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse-free). Based on this, the state-feedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems. Finally, numerical examples are given to illustrate the results.
Authorea (Authorea), 2023
This paper presents two novel mixed-uncertainty state estimators for discretetime descriptor linear systems, namely linear time-varying mixed-uncertainty filter (LTVMF) and linear time-invariant mixed-uncertainty filter (LTIMF). The former estimator is based on the minimum-variance approach, from which quadratic and explicit formulations are derived and addressed to LTI and LTV systems. Both formulations incorporate the knowledge of state linear constraints, such as equality (in the descriptor form) and inequality, to mitigate precision and accuracy issues related to initialization and evolution of the state estimates. The explicit version is developed to reduce the computational burden of quadratic solvers, which is based on a particularity of the state inequality constraints. The LTIMF algorithm is based on the mixed H 2 ∕H ∞ criterion motivated by performing low-cost computations. This speed benefit is originated from a reachability analysis involving constant design matrices. Both LTVMF and LTIMF algorithms solve state-estimation problems in which the uncertainties are combined to yield the so-called mixed-uncertainty vector, which is composed by set-bounded uncertainties, characterized by constrained zonotopes, and stochastic uncertainties, characterized by Gaussian random vectors. As mixed-uncertainty vectors imply biobjective optimization problems, we innovatively present multiobjective arguments to justify the choice of the solution on the Pareto-optimal front. According to these arguments, LTVMF is introduced with a cost normalization, which enables the combination of beyond minimum-variance approaches. Likewise, the mixed H 2 ∕H ∞ criterion of LTIMF is introduced with slack variables to improve the quality of the state estimates. In order to discuss the advantages and drawbacks, the state estimators are tested in two numerical examples.
IEEE Transactions on Signal Processing, 2004
The robust filtering problem for a class of continuous-time uncertain linear descriptor systems with time-varying discrete and distributed delays is investigated. The time delays are assumed to be constant and known. The uncertainties under consideration are norm-bounded, and possible time-varying, uncertainties. Sufficient condition for the existence of an filter is expressed in terms of strict linear matrix inequalities (LMIs). Instead of using decomposition technique, a unified form of LMIs is proposed to show the exponential stability of the augmented systems. The condition for assuring the stability of the "fast" subsystem is implied from the unified form of LMIs, which is shown to be less conservative than the characteristic equation based conditions or matrix norm-based conditions. The suitable filter is derived through a convex optimization problem. A numerical example is given to show the effectiveness of the method.
Linear Algebra and its Applications, 1999
This paper considers robust controllability for uncertain linear descriptor systems with structured perturbations. Necessary and sufficient conditions based on the µ-analysis are obtained by transforming the problem into checking the nonsingularity of a class of uncertain matrices. Also a tight bound is obtained in terms of µ for keeping the closed-loop system regular, impulse-free and stable under a preconstructed static output feedback. An example is given to illustrate the results.
State and Unknown Inputs Estimations for Multi-Models Descriptor Systems
HAL (Le Centre pour la Communication Scientifique Directe), 2012
In this note, the problem of states and unknown inputs estimation of nonlinear descriptor system is considered. The methodology is based on the use of Proportional Integral and Unknown Input Observers. The considered nonlinear descriptor system is transformed into an equivalent multi-models form by using the Takagi-Sugeno (T-S) approach. In this paper, the design methods of both proportional integral observers and unknown inputs observers for descriptor multi-models are described in detail. Sufficient conditions of stability analysis and gain matrices determination are performed by resolving a set of Linear Matrices Inequalities (LMIs). The design method offers all the degrees of design freedom, which can be utilized to achieve various desired system specifications and performances and, thus, has great potentials in applications. A numerical example is employed to show the design procedure of these two observers and illustrate the effect of the proposed approach.
Robust invariant sets and active mode detection for discrete-time uncertain descriptor systems
2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017
In this paper, the computation of robust invariant sets for discrete-time uncertain descriptor systems is investigated. The studied descriptor systems are assumed to be regular and stable subject to unknown but bounded disturbances. The robust invariant sets of both causal and non-causal descriptor systems are studied. Transformations for causal and non-causal descriptor systems are used in the characterization of the effect of the disturbances. For causal descriptor systems, two robust positively invariant (RPI) sets are computed separately. For non-causal descriptor systems, an RPI set and a robust negatively invariant (RNI) set can be found. As a result, the general RPI set of a descriptor system can be obtained from a linear projection image of these two sets. Besides, active mode detection method is proposed based on set invariance theory.