An observer design for linear time-delay systems

Hou, M.; Zı́tek, Pavel; Patton, Ron J.

doi:10.1109/9.981730

Cited by 97 publications

(83 citation statements)

References 16 publications

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“…If rank K (δ ] Φ k+1 = n k+1 = n, then Theorem 2 can be used to judge whether the unknown input is left invertible or not. If, however, rank K (δ ] Φ k+1 = n k+1 < n, then we can follow the same procedure presented in this subsection to compute £ k+1 as (13), Ω k+1 as (14), G ⊥ k+1 as (15), H k+1 as (16) and Y k+2 as (17).…”

Section: Iterative Canonical Formmentioning

confidence: 99%

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Finite-time and asymptotic left inversion of nonlinear time-delay systems

2018

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In this paper we investigate the left invertibility problem for a class of nonlinear time-delay systems. In both cases of time delay systems with and without internal dynamics the invertibility conditions are given. A new approach based on the use of higher order sliding mode observer is developed for finite-time left invertibility and for asymptotic left inversion. Causal and non-causal estimation of the unknown inputs are respectively discussed. The results are illustrated by numerical examples in order to show the efficiency of the method and its limits.Key words: Left inversion, nonlinear system, nonlinear time-delay system, asymptotic left inversion, internal dynamics. IntroductionTime delay systems represent one of the most studied class of systems in control theory. Since the 60', many different problems are studied such as stability and stabilization of time delay systems, observation and observer design, parameter identification, etc. In the present work we are interested in the left invertibility problem of time delay systems with internal dynamics. The problem of unknown inputs recovering from the outputs is crucial. Such a problem has attracted the interest of the control community since it has direct applications in many domains, such as data secure transmission where the unknown input is the message, and fault detection and isolation where the fault is the unknown input. In fact, left invertibility problem has been studied since at least forty five years ago in linear control theory [33] In the literature, an important tool based on non-commutative ring, proposed in [36], is used to analyze nonlinear time delay systems in algebraic framework. Using this framework, many notions are extended to the case of nonlinear time * Corresponding author.Email address: zohra.kader@inria.fr (Zohra Kader). delay systems and many results have already been obtained and published [40], [37]. In the context of constant time delay, the notions of Lie derivatives and relative degree are defined, and the differences between causal and non-causal invertibility are clarified in [38]. The canonical form of invertibility is also given in [39], and in [42] a method for estimating the unknown inputs is proposed. However, the algorithm for left invertibility proposed in [39] was only for system without internal dynamics (see also [4] and [13] and their references). For system with or without time-delay, the main difficulty when the internal dynamics appears is to estimate the state of such dynamics. One interesting solution in order to overcome such a difficulty is to allow the derivative of the unknown inputs [31] with a geometrical approach and with an algebraic one. If, however, the input derivatives are not possible, then it is necessary to compute and analyze the internal dynamics.For nonlinear systems without delay, if the vector fields associated to the inputs verify involutivity property, then the internal dynamics does not depend on the unknown input. However, this rule is not valid for nonlinear systems with...

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Section: Iterative Canonical Formmentioning

confidence: 99%

“…Using this framework, many notions are extended to the case of nonlinear time system in the literature [3], [12], [14], [16], [17], [20] and the high order sliding mode proposed in [22], [23] (see also [10] for unknown input observer) is applied in this paper.…”

Section: Introductionmentioning

confidence: 99%

Finite-time and asymptotic left inversion of nonlinear time-delay systems

2018

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“…The predictor dynamics can now be designed based on time advanced system (8). The dynamics for the predictor is proposed as a copy of the time advanced dynamics (8) plus a term injecting the delayed observer error:…”

Section: Predictor Designmentioning

confidence: 99%

“…It is mandatory first to analyze the state prediction problem, to solve, using causal state feedback, control problems for nonlinear systems with delay at the input [7,8]. In most of the cases, the state prediction problem is related to the pioneering work of state observation [9] or its generalization presented in [10] for delay-free nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Prediction‐Based Control for Nonlinear Systems with Input Delay

Estrada-Sanchez

Velasco-Villa

Rodriguez-Cortes

2017

Mathematical Problems in Engineering

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This work has two primary objectives. First, it presents a state prediction strategy for a class of nonlinear Lipschitz systems subject to constant time delay in the input signal. As a result of a suitable change of variable, the state predictor asymptotically provides the value of the state units of time ahead. Second, it proposes a solution to the stabilization and trajectory tracking problems for the considered class of systems using predicted states. The predictor-controller convergence is proved by considering a complete Lyapunov functional. The proposed predictor-based controller strategy is evaluated using numerical simulations.

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“…Time-delay system with memoryless state observer was presented in [21]. In [22], an observer for linear time-delay systems was designed using coordinate transformations. An observer for linear time-delay systems with unknown input was designed in [23].…”

Section: Observers For Time-delay Systemsmentioning

confidence: 99%

Evaluation of Load Balancing Performance of Parallel Processing Linear Time-Delay Systems

Kabir

Alam²,

Azad³

2015

IJIEEB

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Abstract-Time delays in system states or control may result into unacceptable system operation or uncertainty in specialised technical systems like aircraft control, plant control, robotics etc. The issue of robustness, controllability, traceability, flexible management, reliability, and safety of such systems with time-delays, has been one of the primary research focuses of the last few decades. In parallel computing, different computing subunits share their tasks to balance loads to increase performance and throughput. In order to do so, subsystems have to communicate among themselves, adding further delay on top of existing system delay. It is possible to maintain performance and stability of the whole system, by designing observer for every subsystem in the system, overseeing the system state and compensating for existing time-delay. This paper reviews present literature to identify a linear time-delay system for load balancing and evaluates the stability and load balancing performance of the system with and without an observer. Stability is analysed in terms of oscillation in the system responses and performance is evaluated as the speed of load-balancing operation.

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An observer design for linear time-delay systems

Cited by 97 publications

References 16 publications

Finite-time and asymptotic left inversion of nonlinear time-delay systems

Finite-time and asymptotic left inversion of nonlinear time-delay systems

Prediction‐Based Control for Nonlinear Systems with Input Delay

Evaluation of Load Balancing Performance of Parallel Processing Linear Time-Delay Systems

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