Functional observers design for descriptor systems via LMI: Continuous and discrete-time cases

Darouach, Mohamed; Amato, Francesco; Alma, Marouane

doi:10.1016/j.automatica.2017.08.016

Cited by 36 publications

(34 citation statements)

References 3 publications

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“…From the definition of J, if S = U T U is allowed, according to the Schur Complement lemma, 41 (30) can guarantee J < 0, which means that ||S • T • S −1 || ∞ < 1. Then, we establish that system (28) is asymptotically stable by Lemma 1.…”

Section: Lemma 3 (See the Work Of Chang Et Al 40 )mentioning

confidence: 99%

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Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Yuan

2019

Intl J Robust & Nonlinear

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Summary This paper considers the preview tracking control problem of polytopic uncertain discrete‐time systems with a time‐varying delay subject to a previewable reference signal. First, a model transformation is employed and a discrete‐time system with a time‐invariant delay and an external disturbance is obtained. The difference operator method can be extended to derive an augmented error system that includes future information on the reference signal. Then, a previewable reference signal is fully utilized through reformulation of the output equation while considering the output feedback. Based on the small gain theorem, a static output feedback controller with preview actions is designed such that the output can asymptotically track the reference signal. Finally, numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the paper.

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Section: Lemma 3 (See the Work Of Chang Et Al 40 )mentioning

confidence: 99%

“…It should be mentioned that the introduction of the scalar parameter is not necessary to derive our results, but the selection of provides an extra free dimension in (41).…”

Section: From Lemma 4 Theorem 1 Holdsmentioning

confidence: 99%

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Yuan

2019

Intl J Robust & Nonlinear

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“…In the existing literature on the observer design of linear descriptor systems, the impulse observability is a natural assumption on system operators (see the works of Kumar et al and Darouach and Boutayeb and the references therein). Recently, the impulse observability of linear descriptor systems has been appropriately extended or modified as one of the sufficient conditions to design Luenberger‐type observers for linear systems with unknown inputs and to design functional observers . The impulse observability implies that there exists an output feedback such that the closed‐loop system is impulse free and can be seen as an observer matching condition for a descriptor system.…”

Section: Basic Assumptions and Transformationsmentioning

confidence: 99%

“…Recently, the impulse observability of linear descriptor systems has been appropriately extended or modified as one of the sufficient conditions to design Luenberger-type observers for linear systems with unknown inputs 18 and to design functional observers. 19 The impulse observability implies that there exists an output feedback such that the closed-loop system is impulse free and can be seen as an observer matching condition for a descriptor system.…”

Section: Basic Assumptions and Transformationsmentioning

confidence: 99%

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Unknown inputs observer design for descriptor systems with monotone nonlinearities

Gupta

Tomar

Darouach

2018

Intl J Robust & Nonlinear

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Summary This paper is devoted to the reduced‐order unknown inputs observer design problem for a class of descriptor systems having generalized monotone nonlinearities. The underlying system is considered in general rectangular form with unknown inputs in dynamic and in output equations. Under some basic assumptions on system parameters, sufficient conditions for the existence of observers are proved by showing the stability of their error dynamics. The case where nonlinearity appears in output equation is also considered. The importance of the work is illustrated by real‐life and academic examples.

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Robust observer design for a class of discrete‐time nonlinear singular systems with persistent disturbances

Coutinho

Souza

Kinnaert

et al. 2020

Adaptive Control & Signal

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SummaryThis article addresses the design of a nonlinear observer for nonlinear uncertain discrete‐time descriptor systems. The nonlinearities that appear in both state and output equations fulfill a Lipschitz‐like condition locally. Besides, the parametric uncertainties can affect the state dynamics as well as the input and output channels. The design methodology ensures input‐to‐state stability of the observer while minimizing an upper bound on a peak‐to‐peak performance index relating the disturbances/parametric uncertainties and the error in estimating a given performance signal. The observer design is cast as a convex optimization problem involving a set of linear matrix inequalities subject to a linear matrix equality constraint. The effectiveness of the proposed method is illustrated by numerical examples.

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Functional observers design for descriptor systems via LMI: Continuous and discrete-time cases

Cited by 36 publications

References 3 publications

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Unknown inputs observer design for descriptor systems with monotone nonlinearities

Robust observer design for a class of discrete‐time nonlinear singular systems with persistent disturbances

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